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Five hundred people attended the band concert. For that concert, the band gets 70% of the ticket price. Each ticket costs $30 and there are 4 members of the band. How much did each band member get from that concert? | First, let's calculate the total revenue from ticket sales:
500 people * $30 per ticket = $15,000
Next, we calculate the band's share of the revenue:
70% of $15,000 = 0.70 * $15,000 = $10,500
Now, we divide the band's share by the number of band members to find out how much each member gets:
$10,500 / 4 members = ... |
A certain store sold pens for $0.45 each, pencils for $0.35 each, and erasers for $0.30 each. If a customer purchased a combination of pens, pencils, and erasers from the store for a total of $7.80, what is the total number of pens, pencils, and erasers the customer purchased? | Let's denote the number of pens purchased as P, the number of pencils as L, and the number of erasers as E. We can set up the following equation based on the given prices and total cost:
0.45P + 0.35L + 0.30E = 7.80
This equation represents the total cost of the pens, pencils, and erasers combined. However, with just... |
Sachin is younger than Rahul by some years. The ratio of their ages is 7 : 9. Sachin is 63 years old. How many years younger is Sachin than Rahul? | Let's denote Sachin's age as S and Rahul's age as R. According to the information given, the ratio of their ages is 7:9, and Sachin's age is 63 years.
So we can write the ratio as:
S/R = 7/9
We know that Sachin's age (S) is 63, so we can substitute S with 63 in the ratio:
63/R = 7/9
Now we can solve for R (Rahul's a... |
Find the expenditure on digging a well 14 m deep and of 3 m diameter at a certain rate per cubic meter, if the total cost is Rs. 1781.28. What is the rate per cubic meter? | To find the rate per cubic meter, we first need to calculate the volume of the well that was dug. The well is in the shape of a cylinder, so we can use the formula for the volume of a cylinder:
Volume (V) = π * r^2 * h
where r is the radius of the cylinder (half of the diameter) and h is the height (or depth) of the ... |
At the opening of a trading day at a certain stock exchange, the price per share of stock M was $25. If the price per share of stock M increased by 12.00000000000001% during the day, what was the closing price per share of stock M? | To find the closing price per share of stock M, we need to calculate the increase in price and then add it to the opening price.
The increase in price is 12.00000000000001% of the opening price of $25.
Increase = (12.00000000000001/100) * $25
Increase = 0.1200000000000001 * $25
Increase = $3.0000000000000025
Now, ... |
An error of 4% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? | Let the actual side of the square be \( S \).
When an error of 4% in excess is made while measuring the side, the measured side becomes \( S' = S + 0.04S = S(1 + 0.04) = 1.04S \).
The actual area of the square is \( A = S^2 \).
The calculated area with the error in measurement is \( A' = (S')^2 = (1.04S)^2 = 1.0816S... |
John has Rs 360 for his expenses. If he exceeds his days by 4 days, he must cut down daily expenses by Rs 3. How many days is John's tour program? | Let's denote the number of days in John's tour program as \( d \) and his daily expenses as \( e \).
According to the problem, John has Rs 360 for his expenses. So, if he spends \( e \) rupees per day for \( d \) days, we have:
\[ e \cdot d = 360 \] ... (1)
If John exceeds his days by 4, he will have to cut down his ... |
After 10% of the inhabitants of a village disappeared, a panic set in during which a certain percentage of the remaining inhabitants left the village. At that time, the population was reduced to 4725. The number of original inhabitants was approximately 7000. What was the percentage of the remaining inhabitants that le... | Let's denote the original number of inhabitants as \( X \).
After 10% disappeared, the number of inhabitants remaining would be \( 90\% \) of \( X \), which can be written as \( 0.9X \).
Let's denote the percentage of the remaining inhabitants that left during the panic as \( P \). This means that \( (100 - P)\% \) o... |
There are 250 blocks. 13 more blocks are added, and then the total quantity of blocks is doubled. How many blocks are there in the end? | First, we add the 13 blocks to the initial 250 blocks:
250 blocks + 13 blocks = 263 blocks
Next, we double the total quantity of blocks:
263 blocks × 2 = 526 blocks
So, in the end, there are $\boxed{526}$ blocks. |
An uneducated retailer marks all his goods at 65% above the cost price and thinking that he will still make 25% profit, offers a discount of a certain percentage on the marked price. His actual profit on the sales is 23.75%. What percentage discount did he offer on the marked price? | Let's assume the cost price (CP) of the goods is $100.
The retailer marks up his goods by 65%, so the marked price (MP) is:
MP = CP + (65% of CP)
MP = $100 + ($100 * 0.65)
MP = $100 + $65
MP = $165
The retailer wants to make a 25% profit, so he offers a discount (D%) on the marked price. Let's assume the selling pric... |
Keats library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 32% of the total number of books in the library. Prior to the purchase, only 20% of the books in... | Let's denote the original number of books in the library as \( B \) and the original number of biographies as \( b \). We are told that \( b \) is 20% of \( B \), so we can write:
\[ b = 0.20B \]
Let's denote the number of new biographies purchased as \( n \). After the purchase, the number of biographies is \( b + n... |
Jake is retrieving the notes on a communal board, putting all of the red notes in the complaints bin and all of the blue notes in the compliments bin. The red notes were in some rows with 6 notes in each row. There are 2 blue notes under each of the red notes, as well as another 10 blue notes scattered at the bottom of... | Let's denote the number of rows of red notes as R.
Each row of red notes has 6 red notes, so the total number of red notes is 6R.
For each red note, there are 2 blue notes. Therefore, the total number of blue notes corresponding to the red notes is 2 * 6R = 12R.
Additionally, there are 10 more blue notes scattered a... |
Marie starts with some erasers. She loses 42 erasers and ends up with 53 erasers. How many erasers did Marie start with? | If Marie ends up with 53 erasers after losing 42, we can find out how many she started with by adding the 42 erasers she lost back to the 53 she ended up with.
So, Marie started with 53 + 42 = $\boxed{95}$ erasers. |
A man is 30 years older than his son. In 5 years, his age will be triple the age of his son. What is the present age of the son? | Let's denote the present age of the son as S and the present age of the father as F.
According to the information given:
F = S + 30 (since the father is 30 years older than his son)
In 5 years, the son's age will be S + 5 and the father's age will be F + 5. At that time, the father's age will be triple the son's age... |
p and q invested in a business. The profit earned was divided in the ratio 2 : 3. If q invested Rs 45,000, how much did p invest in the business? | Let's denote the amount invested by p as "P" and the amount invested by q as "Q". According to the problem, Q is Rs 45,000.
The profit is divided in the ratio of 2:3 between p and q. This means that for every 2 parts of profit that p receives, q receives 3 parts.
Since the investments of p and q are directly proport... |
What least number should be subtracted from 997 so that the remainder when divided by 5, some number, and 11 will leave in each case the same remainder 3? The second divisor is 9. | To find the least number that should be subtracted from 997 so that the remainder when divided by 5, 9, and 11 will leave the same remainder of 3, we need to find a number that is a common multiple of 5, 9, and 11, and then add 3 to it (since we want a remainder of 3).
The least common multiple (LCM) of 5, 9, and 11 c... |
There are 25 roses in a garden. There are 40 tulips and some daisies. 75% of flowers are not roses. How many daisies are there in the garden? | If 75% of the flowers are not roses, then 25% of the flowers are roses. Since we know there are 25 roses, we can use this information to find the total number of flowers in the garden.
Let's call the total number of flowers in the garden F. Since 25% of F is equal to 25 (the number of roses), we can write the equation... |
A number whose fifth part increased by 4 is equal to its fourth part diminished by 10. What is the number? | Let's denote the number as \( x \).
According to the problem, the fifth part of the number increased by 4 is equal to the fourth part of the number diminished by 10. This can be written as an equation:
\[ \frac{x}{5} + 4 = \frac{x}{4} - 10 \]
To solve for \( x \), we first need to get rid of the fractions by finding... |
A wall clock rings n times a day at non-equal intervals. The time between the first two rings is x hours, and the time between each subsequent pair of rings increases by y hours. Considering that the clock rings for the first time at 12:00 PM (noon), find an expression for the time between the last two rings, in terms ... | Let's denote the time between the last two rings as T.
The first ring is at 12:00 PM, and the second ring is x hours after that. The third ring is x + y hours after the second ring, the fourth ring is x + 2y hours after the third ring, and so on.
We can see that the time between each subsequent pair of rings forms an... |
Nell collects baseball cards. She initially had 304.5 cards. Her friend Jeff gave her 276.25 cards. How many cards does Nell now have? | To find out how many cards Nell now has, we need to add the number of cards she initially had to the number of cards her friend Jeff gave her.
Nell initially had 304.5 cards.
Jeff gave her 276.25 cards.
So, the total number of cards Nell now has is:
304.5 + 276.25 = 580.75 cards
Nell now has $\boxed{580.75}$ baseb... |
John has 2 umbrellas in his house and some in the car. If they cost $8 each, he paid $24 in total. How many umbrellas does John have in his car? | If John paid $24 in total for the umbrellas and each umbrella costs $8, we can find out the total number of umbrellas he bought by dividing the total amount paid by the cost of each umbrella.
Total umbrellas = Total amount paid / Cost per umbrella
Total umbrellas = $24 / $8
Total umbrellas = 3
John has 2 umbrellas in... |
a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was $ 1480 ? | Let's denote the daily wages of A, B, and C as $3x, $4x, and $5x respectively, according to the given ratio of 3:4:5.
Now, we know that A worked for 6 days, B for 9 days, and C for 4 days. So, their total earnings can be calculated as follows:
Total earnings of A = 6 days * $3x
Total earnings of B = 9 days * $4x
Tota... |
An athlete runs a 200-meter race that includes elevation changes and faces wind resistance throughout the course. The elevation increases by 5 meters in the first 50 meters, remains constant for the next 50 meters, and then decreases by 5 meters over the final 100 meters. The wind is blowing from the front with a speed... | To calculate the average speed of the athlete during the race, we need to divide the total distance covered by the total time taken to cover that distance.
The total distance covered is 200 meters, and the total time taken is 40 seconds.
Average speed = Total distance / Total time
Average speed = 200 meters / 40 seco... |
Ryan works in an office that has an even number of men and women working there. Ryan participates in a meeting composed of 4 men and 6 women who are pulled from the office floor. This reduces the number of women working on the office floor by 20%. How many people work at Ryan's office? | Let's denote the total number of men in the office as M and the total number of women as W. Since the office has an even number of men and women, we can say that M = W.
From the information given, when 6 women are pulled from the office floor for the meeting, it reduces the number of women working on the office floor ... |
Matt needs to buy new plates for his home. He only wants to do dishes once a week. Three days a week it is only him and his son eating and they use 1 plate each. On the remainder of the days, his parents join them and everyone uses 2 plates that day. How many plates does he need to buy? | For the three days when it's just Matt and his son, they use 1 plate each, so that's 3 days * 2 plates/day = 6 plates.
On the other four days when his parents join them, there are 4 people eating and everyone uses 2 plates, so that's 4 days * 4 people * 2 plates/person = 32 plates.
Adding the two amounts together, Ma... |
Jo-Bob hopped into the hot air balloon and pulled on the lift chain, which caused the balloon to rise. When the lift chain was pulled, the balloon would rise at a rate of 50 feet per minute. But when the chain was not being pulled, the balloon would slowly descend at a rate of 10 feet per minute. During his balloon rid... | Let's denote the number of minutes Jo-Bob pulled the chain for the first time as \( x \).
During the time he pulled the chain, the balloon rose at a rate of 50 feet per minute. So, for the first \( x \) minutes, the balloon rose \( 50x \) feet.
After he released the chain for 10 minutes, the balloon descended at a ra... |
Beka flew 425 miles to her first layover, then 320 miles to her second layover, and finally 387 miles to visit her aunt. Jackson flew 250 miles to his first layover, 170 miles to his second layover, 353 miles to his third layover, and 201 miles to visit his aunt. How many more miles did Beka fly than Jackson in total? | To find out how many more miles Beka flew than Jackson, we first need to calculate the total miles each person flew.
Beka's total miles:
425 (first layover) + 320 (second layover) + 387 (to visit aunt) = 1132 miles
Jackson's total miles:
250 (first layover) + 170 (second layover) + 353 (third layover) + 201 (to visit... |
There are some school days in the academic year. Aliyah packs a lunch half the time. Becky packs her lunch half as much as Aliyah. Becky packs her lunch 45 days a year. How many school days are there in the academic year? | If Becky packs her lunch half as much as Aliyah and she packs her lunch 45 days a year, then Aliyah packs her lunch twice as many days as Becky.
So, Aliyah packs her lunch for 45 days * 2 = 90 days a year.
Since Aliyah packs her lunch half the time, the total number of school days in the academic year would be twice... |
John purchased 1325 large bottles at $1.89 per bottle and 750 small bottles at a certain price per bottle. The approximate average price paid per bottle was $1.7057. What was the price per small bottle? | Let's denote the price per small bottle as \( P \).
John purchased 1325 large bottles at $1.89 each, so the total cost for the large bottles is:
\( 1325 \times 1.89 \)
He also purchased 750 small bottles at \( P \) dollars each, so the total cost for the small bottles is:
\( 750 \times P \)
The total number of bottl... |
p, q, and r have Rs. 6000 among themselves. r has a certain fraction of the total amount with p and q. r has Rs. 2400. What is the fraction of the total amount that r has? | The total amount among p, q, and r is Rs. 6000.
r has Rs. 2400.
To find the fraction of the total amount that r has, we divide the amount r has by the total amount:
Fraction that r has = Amount r has / Total amount
Fraction that r has = 2400 / 6000
Now, we simplify the fraction:
Fraction that r has = 2/5
So, r ha... |
Calen originally had 5 more pencils than does Caleb, and Caleb has 3 less than twice as many pencils as does Candy. Calen lost some pencils, which left him with 10 pencils. Candy has 9 pencils. How many pencils did Calen lose? | Let's denote the number of pencils Caleb has as P_Caleb, and the number of pencils Candy has as P_Candy. According to the problem, Candy has 9 pencils, so P_Candy = 9.
The problem states that Caleb has 3 less than twice as many pencils as Candy. So we can write this as:
P_Caleb = 2 * P_Candy - 3
Substituting the valu... |
i have 150 pieces of cake . there are 50 friends in my house . i would like to give each friend the same amount of cake , how much should i give to each friend ? | If you have 150 pieces of cake and you want to give an equal amount to each of your 50 friends, you would divide the total number of cake pieces by the number of friends:
150 pieces of cake ÷ 50 friends = 3 pieces of cake per friend
So, you should give each friend $\boxed{3}$ pieces of cake. |
Michael’s largest watermelon weighs 12 pounds. His neighbor, Clay, grew a watermelon that is 1.5 times heavier than Michael's. Their mutual friend, John, grew a watermelon that is half the size of Clay's. Another friend, Emily, grew a watermelon that is 0.75 times the size of John's. Finally, their friend Sophie grew a... | Let's calculate the weight of each person's watermelon step by step:
1. Michael's watermelon weighs 12 pounds.
2. Clay's watermelon is 1.5 times heavier than Michael's, so:
Clay's watermelon weight = 1.5 * Michael's watermelon weight
Clay's watermelon weight = 1.5 * 12 pounds
Clay's watermelon weight = 18 po... |
Real numbers $a$ and $b$ are chosen with $1<a<b$ such that no triangle with positive area has side lengths $1, a,$ and $b$ or $\tfrac{1}{b}, \tfrac{1}{a},$ and X$. The smallest possible value of $b$ is 2. What is the value of unknown variable X? | To solve the problem, we need to determine the value of \( X \) such that no triangle with positive area can have side lengths \( \frac{1}{b}, \frac{1}{a}, \) and \( X \). We start by analyzing the given conditions and using the triangle inequality.
### Step 1: Analyzing the first set of side lengths \( 1, a, b \)
For... |
Having scored 98 runs in the 19th inning, a cricketer increases his average score by a certain amount. His average score after 19 innings is 26. By how much did his average score increase? | Let's denote the cricketer's average score after 18 innings as A. This means that the total runs scored by the cricketer after 18 innings would be 18A.
After scoring 98 runs in the 19th inning, his total runs become 18A + 98.
We are given that the average score after 19 innings is 26. Therefore, the total runs after ... |
if an object travels 80 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet ) | To find the object's speed in miles per hour, we first need to convert the distance traveled from feet to miles and the time from seconds to hours.
First, convert the distance from feet to miles:
80 feet * (1 mile / 5280 feet) = 80 / 5280 miles
80 / 5280 = 0.015151515 miles (approximately)
Next, convert the time from... |
Let solution E contain 2.7 percent of liquid X by weight. Suppose a mixture is prepared by mixing 400 grams of solution A, which contains 0.8 percent of liquid X; 700 grams of solution B, which contains 1.8 percent; 500 grams of solution C, which contains 1.3 percent; and 600 grams of solution D, which contains 2.4 per... | First, let's calculate the amount of liquid X in each solution before they are mixed together.
Solution A (400 grams) contains 0.8% liquid X:
0.008 * 400g = 3.2g of liquid X
Solution B (700 grams) contains 1.8% liquid X:
0.018 * 700g = 12.6g of liquid X
Solution C (500 grams) contains 1.3% liquid X:
0.013 * 500g = 6... |
A teacher is making packed lunches for a field trip. Each student needs a certain number of sandwiches, and will travel in a group with 5 other students. There are a total of 5 groups. The teacher needs 120 pieces of bread to make enough sandwiches for all the students. How many sandwiches does each student need? | Let's start by calculating the total number of sandwiches that can be made with 120 pieces of bread. Since each sandwich requires 2 pieces of bread, we divide 120 by 2 to get the total number of sandwiches:
120 pieces of bread / 2 pieces of bread per sandwich = 60 sandwiches
Now, we know there are 5 groups of student... |
a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 50 % of which are not silver , what percentage of total number of cars are silver ? | First, let's find out how many silver cars are initially on the lot:
20% of 40 cars = 0.20 * 40 = 8 silver cars
Now, let's find out how many non-silver cars are in the new shipment:
50% of 80 cars = 0.50 * 80 = 40 non-silver cars
Since 50% of the new shipment is not silver, the other 50% must be silver:
50% of 80 ... |
A boy wanted to calculate his speed on his bike. His starting point was 350 meters from the turning point. He made the round trip 5 times in 30 minutes. What was the boy's speed in kilometers per hour? | First, we need to calculate the total distance the boy traveled. Since he made the round trip 5 times, and one round trip is the distance to the turning point and back, we have:
Distance for one round trip = Distance to turning point + Distance back to starting point
= 350 meters + 350 meter... |
At a supermarket, John spent 1/5 of his money on fresh fruits and vegetables, 1/3 on meat products, 1/10 on bakery products, and 1/6 on dairy products. He also spent the remaining amount on both candy and a magazine. The magazine costs $3.75, and the total spent on candy and the magazine combined is $14.50. How much di... | Let's denote the total amount of money John had as X.
According to the problem, John spent:
- 1/5 of his money on fresh fruits and vegetables, which is (1/5)X.
- 1/3 of his money on meat products, which is (1/3)X.
- 1/10 of his money on bakery products, which is (1/10)X.
- 1/6 of his money on dairy products, which is ... |
Phil started his day with $40. He bought a slice of pizza for $2.75, a soda for $1.50, and a pair of jeans. He has nothing but quarters left of his original money, and he now has 97 quarters. How much did the pair of jeans cost? | Phil started with $40 and spent $2.75 on pizza and $1.50 on soda. Let's first calculate the total amount spent on these items:
Pizza: $2.75
Soda: $1.50
Total spent on pizza and soda: $2.75 + $1.50 = $4.25
Now, let's subtract this amount from the original $40 to find out how much money Phil had before buying the jeans... |
For a recipe for triple berry pie, it calls for cups of a certain fruit, raspberries, and blueberries in a ratio of 1 : 2 : 3. You will need 6 total cups of fruit to make the pie. Which fruit has the smallest proportion in the recipe? | The ratio given for the fruits is 1:2:3, which means for every 1 part of the first fruit, there are 2 parts of the second fruit, and 3 parts of the third fruit. To find out how many cups of each fruit are needed, we first need to find the total number of parts in the ratio.
1 (for the first fruit) + 2 (for the second ... |
Emily is on a flight from New York to Hawaii that is 10 hours long. To kill time, she watches 3 TV episodes that are each 25 minutes long. Then she sleeps for 4 and a half hours. Then she watches 2 movies that are each an hour and 45 minutes long. After doing all these things, assuming there is no break time between ac... | First, let's calculate the total time Emily has spent on her activities in minutes.
3 TV episodes at 25 minutes each:
3 episodes * 25 minutes/episode = 75 minutes
Sleeping for 4 and a half hours:
4.5 hours * 60 minutes/hour = 270 minutes
2 movies at 1 hour and 45 minutes each:
1 hour 45 minutes = 105 minutes/movie
2... |
a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ? | Let's denote the length of the platform as \( L \).
When the train crosses a signal pole, it only needs to cover its own length, which is 300 m. It does this in 24 seconds. Therefore, the speed of the train (\( V \)) can be calculated as:
\[ V = \frac{\text{Distance}}{\text{Time}} = \frac{300 \text{ m}}{24 \text{ sec... |
A bag was originally priced at $500. A week after, the price was reduced by 5%. Since the bag was still not sold, the selling price was reduced by 4% a month after. How much was the total reduction from the original selling price? | First, let's calculate the price reduction after the first week.
5% of $500 is:
0.05 * $500 = $25
So, the price after the first reduction is:
$500 - $25 = $475
Next, let's calculate the price reduction a month after.
4% of $475 is:
0.04 * $475 = $19
So, the price after the second reduction is:
$475 - $19 = $456
N... |
Mike went to some basketball games this year, but missed 41. He went to 39 games last year. Mike went to a total of 54 basketball games. How many basketball games did Mike go to this year? | If Mike went to a total of 54 basketball games and he went to 39 games last year, then the number of games he went to this year would be the total minus the number he went to last year.
So, the calculation would be:
54 (total games) - 39 (last year's games) = 15 (this year's games)
Therefore, Mike went to $\boxed{15... |
Marissa has 4.5 feet of ribbon that she wants to use to tie some boxes. If 1 foot of ribbon is left after Marissa uses 0.7 feet of ribbon to tie each box, find out how many boxes she tied? | Marissa has 4.5 feet of ribbon in total. She uses 0.7 feet of ribbon to tie each box. After tying the boxes, she has 1 foot of ribbon left.
First, we need to find out how much ribbon she used to tie the boxes. We do this by subtracting the ribbon left from the total ribbon she had:
4.5 feet (total ribbon) - 1 foot (r... |
James took a 3-hour bike ride. In the second hour, he traveled 12 miles. If he traveled 25 percent farther in the third hour than he did in the second hour, James traveled 37 miles during the entire ride. What was the percentage increase in distance traveled from the first hour to the second hour? | Let's denote the distance James traveled in the first hour as \( D_1 \), in the second hour as \( D_2 \), and in the third hour as \( D_3 \).
We are given that \( D_2 = 12 \) miles.
In the third hour, he traveled 25 percent farther than he did in the second hour. To find \( D_3 \), we calculate 25 percent of \( D_2 \... |
In a tea shop, the cost per pound of green tea, black tea, and coffee were the same in January. In February, the price of coffee shot up by 75%, that of black tea increased by 45% and the price of green tea dropped by 60%. In March, the pricing trend continued and coffee got an additional 60% increase, black tea got a ... | Let's denote the cost per pound of green tea, black tea, and coffee in January as \( C \) dollars.
In February:
- The price of coffee increased by 75%, so it became \( C + 0.75C = 1.75C \).
- The price of black tea increased by 45%, so it became \( C + 0.45C = 1.45C \).
- The price of green tea dropped by 60%, so it b... |
A person travels equal distances with speeds of 6 km/hr, 12 km/hr, and 18 km/hr. They take some time to travel the distances, and the total distance is approximately 1800 meters. How many minutes does it take for the person to travel the distances? | Let's denote the equal distance traveled at each speed as \( d \) kilometers. Since the total distance is approximately 1800 meters, we can convert this to kilometers by dividing by 1000:
\( 1800 \text{ meters} = 1.8 \text{ kilometers} \)
Since the person travels this distance three times (once at each speed), we hav... |
The owner of a furniture shop charges his customer 24% more than the cost price. A customer paid a certain amount for a computer table, and the cost price of the computer table was Rs. 6625. How much did the customer pay for the computer table? | To find out how much the customer paid for the computer table, we need to calculate the 24% markup on the cost price and then add it to the cost price.
First, let's calculate the 24% markup on the cost price of Rs. 6625.
Markup = (24/100) * Cost Price
Markup = (24/100) * 6625
Markup = 0.24 * 6625
Markup = 1590
Now, ... |
The bus driver drives an average of 2 hours each day for a certain number of days a week. From Monday to Wednesday he drove at an average speed of 12 kilometers per hour, and from Thursday to Friday at an average speed of 9 kilometers per hour. The driver traveled 108 kilometers during these days. How many days a week ... | Let's denote the number of days the driver drove from Monday to Wednesday as \( D_{MW} \) and the number of days from Thursday to Friday as \( D_{TF} \).
From Monday to Wednesday, the driver drove at an average speed of 12 km/h for 2 hours each day. Therefore, the total distance covered from Monday to Wednesday is:
\[... |
At the end of year x, automobile installment credit accounted for a certain percentage of all outstanding consumer installment credit. At that time, automobile finance companies extended $50 billion of credit, or 1/4 of the automobile installment credit. There were $465.1162790697675 billion of consumer installment cre... | To find the percentage of consumer installment credit accounted for by automobile installment credit, we first need to determine the total amount of automobile installment credit.
We know that automobile finance companies extended $50 billion of credit, which represents 1/4 of the total automobile installment credit. ... |
Mike had 16 video games, but 8 of them weren't working. He decided to sell the working games at different prices. The prices for the working games are as follows: $6, $7, $9, $5, $8, $10, $12, and $11. How much money could he earn by selling all the working games? | To find out how much money Mike could earn by selling all the working games, we need to add up the prices of each working game.
The prices are: $6, $7, $9, $5, $8, $10, $12, and $11.
Let's add them up:
$6 + $7 + $9 + $5 + $8 + $10 + $12 + $11 = $68
So, Mike could earn $\boxed{\$68}$ by selling all the working gam... |
In a certain country store, there are three kinds of bottled drinks. A cola, which costs $3, a juice for $1.5, and water for $1 per bottle. One day the store was able to sell 15 bottles of cola, some bottles of water, and 12 bottles of juice. The shop earned $88. How many bottles of water were sold? | Let's denote the number of bottles of water sold as W.
The total earnings from the cola sold is 15 bottles * $3/bottle = $45.
The total earnings from the juice sold is 12 bottles * $1.5/bottle = $18.
The total earnings from the water sold would then be W bottles * $1/bottle = $W.
The total earnings from all the drin... |
A train of a certain length crosses an electric pole in 3.9996800255979523 seconds, if its speed is 90 km/hr. How long is the train? | To find the length of the train, we need to convert the speed from km/hr to m/s and then multiply it by the time it takes to cross the electric pole.
First, let's convert the speed from km/hr to m/s:
Speed in m/s = Speed in km/hr * (1000 m / 1 km) * (1 hr / 3600 s)
Speed in m/s = 90 * (1000 / 1) * (1 / 3600)
Speed i... |
If Lawrence worked 8 hours each day on Monday, Tuesday, and Friday, and 5.5 hours on both Wednesday and Thursday, what would be the equal number of hours he would work each day? | To determine the equal number of hours Lawrence would work each day, we first need to calculate the total number of hours he worked over the week. We will then divide this total by the number of days in the week.
1. Calculate the total hours worked on Monday, Tuesday, and Friday:
Lawrence worked 8 hours each day on... |
If m is an integer such that (-2)^2m = 2^(12-m), what is the value of m? | To find the value of m, we need to equate the exponents of the bases on both sides of the equation, since the bases are powers of 2.
Given the equation:
(-2)^(2m) = 2^(12-m)
First, let's simplify the left side of the equation. Since -2 is raised to an even power (2m), the result will be positive. Therefore, we can wr... |
Nina has exactly enough money to purchase 10 widgets. If the cost of each widget were reduced by $ 1.75, then Nina would have exactly enough money to purchase 14 widgets. How much money does Nina have? | Let's call the original cost of each widget "W" and the total amount of money Nina has "M".
From the information given, we can set up the following equations:
1) The cost of 10 widgets at the original price is equal to the amount of money Nina has:
10W = M
2) If the cost of each widget is reduced by $1.75, the new c... |
Simon, Gerry, Micky, and Darryl want to have a race with handmade miniature rafts. Simon's raft needs 36 sticks, Gerry's raft needs two-thirds of the number of sticks that Simon needs, Micky's raft needs 9 sticks more than Simon and Gerry's rafts combined, and Darryl's raft needs one more stick than the total needed fo... | Let's calculate the number of sticks each boy needs for their raft:
Simon's raft needs 36 sticks.
Gerry's raft needs two-thirds of the number of sticks that Simon needs, so:
Gerry's raft = 2/3 * 36 = 24 sticks.
Micky's raft needs 9 sticks more than Simon and Gerry's rafts combined, so:
Micky's raft = (Simon's raft +... |
If an object travels some distance in 2 seconds, the object's approximate speed is 68.18181818181819 miles per hour. (note: 1 mile = 5280 feet) What is the distance the object traveled? | To find the distance the object traveled, we first need to convert the speed from miles per hour to feet per second, since the time given is in seconds.
1 mile per hour is equivalent to 5280 feet per hour. To convert to feet per second, we divide by 3600 (the number of seconds in an hour):
\[ \text{Speed in feet per ... |
two stations a and b are 155 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ? | Let's calculate the distance covered by the first train from station A before the second train starts from station B.
The first train starts at 7 a.m. and the second train starts at 8 a.m., so there is a 1-hour difference. In this 1 hour, the first train would have covered a distance of 20 km/h * 1 hour = 20 km.
Now,... |
The ratio of flour to water to sugar in a recipe is 8 : 4 : 3. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. The new recipe calls for a certain amount of water and it requires 6 cups of sugar. How much water does the ... | Let's first understand the original recipe's ratios:
Flour : Water : Sugar = 8 : 4 : 3
Now, according to the new recipe, we need to double the ratio of flour to water and halve the ratio of flour to sugar.
Original flour to water ratio is 8:4, which simplifies to 2:1. Doubling this ratio gives us 4:1.
Original flou... |
Convert the decimal number 199 to base 2. Let x represent the number of zeros and y represent the number of ones in the base 2 representation. What is the value of y minus x? | To convert the decimal number 199 to its base 2 (binary) representation, we repeatedly divide the number by 2 and keep track of the remainders. The binary representation is constructed by reading the remainders from bottom to top.
Let's go through the steps:
1. \(199 \div 2 = 99\) with a remainder of \(1\)
2. \(99 \d... |
Determine the area of a trapezoid with bases 4 m and 7 m, and a height of 5 m. | The area of a trapezoid can be calculated using the formula:
Area = (1/2) * (base1 + base2) * height
where base1 and base2 are the lengths of the two parallel bases, and height is the distance between the bases (the height of the trapezoid).
Given:
base1 = 4 m
base2 = 7 m
height = 5 m
Plugging these values into the... |
If a certain percentage of a number is 160, and 30% of that number is 120, what is the percentage that corresponds to 160? | Let's call the number we're looking for "N".
According to the information given, 30% of N is 120. We can write this as:
0.30 * N = 120
To find N, we divide both sides of the equation by 0.30:
N = 120 / 0.30
N = 400
Now that we have the value of N, we can find the percentage that corresponds to 160. Let's call thi... |
Some friends went to a hotel and decided to pay the bill amount equally. 5 of them could pay Rs. 100 each, as a result, one friend had to pay Rs. 100 extra than his share. The friend paid Rs. 220. How many friends were there in total? | Let's denote the total number of friends as \( n \).
According to the information given, if 5 friends could pay Rs. 100 each, then the total amount they could pay is \( 5 \times 100 = Rs. 500 \).
One friend had to pay Rs. 100 extra than his share, and he paid Rs. 220. This means his share was \( 220 - 100 = Rs. 120 \... |
if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is | Let's denote the actual distance traveled by the person as \( D \) km.
If the person walks at 10 km/hr, the time taken to travel the actual distance \( D \) would be \( \frac{D}{10} \) hours.
If the person walks at 14 km/hr, the time taken to travel the actual distance \( D \) plus the additional 20 km would be \( \f... |
Ahmed has 8 orange trees and four times as many apple trees in his orchard as Hassan. Hassan has one apple tree and a certain number of orange trees, and they both have only apple and orange trees in their orchards. There are 9 more trees in Ahmed's orchard than in Hassan's. How many orange trees does Hassan have? | Let's denote the number of orange trees Hassan has as \( O \).
Ahmed has 8 orange trees and four times as many apple trees as Hassan. Since Hassan has one apple tree, Ahmed has \( 4 \times 1 = 4 \) apple trees.
The total number of trees in Ahmed's orchard is the sum of his orange and apple trees, which is \( 8 + 4 = ... |
The zoo receives variable rates of visitors entering the zoo every hour. Let's say the number of visitors for each hour are as follows (in the order of hours):
50, 70, 90, 100, 70, 60, 80, 50.
The visitors tend to divide their time across multiple exhibits. The percentage of visitors going to the gorilla exhibit, the... | To calculate the total number of visitors to the gorilla exhibit in one day, we need to multiply the number of visitors each hour by the percentage of visitors that go to the gorilla exhibit during that hour and then sum up all the values.
Here's the calculation for each hour:
1st hour: 50 visitors * 80% = 50 * 0.8 =... |
A store had 50 oranges in a bin. They threw away 40 of the old ones and put some new ones in the bin. Now, there are 34 oranges in the bin. How many new oranges did they put in the bin? | The store started with 50 oranges and threw away 40, leaving them with 10 oranges. After adding some new ones, there are now 34 oranges in the bin. To find out how many new oranges were added, we subtract the number of oranges left after throwing away the old ones from the total number of oranges now in the bin:
34 (t... |
An author of a book got 6% of the total sales of the paper cover version of his books and 12% of the total sales of the hardcover version. If 32,000 copies of the paper cover version were sold at a certain price each and 15,000 copies of the hardcover version were sold at $0.40 each, and the author earned $1104, what w... | Let's denote the price of each paper cover version as P dollars.
The author earns 6% of the total sales of the paper cover version, so the total earnings from the paper cover version are:
0.06 * P * 32,000
The author earns 12% of the total sales of the hardcover version, and since we know the price of each hardcover ... |
Ben works 8-hour shifts in a furniture shop. It takes him 5 hours to build 1 rocking chair, 3 hours to build 1 dining chair, and 6 hours to build 1 armchair. In one day, he builds 2 rocking chairs and 1 dining chair. How many rocking chairs, dining chairs, and armchairs can he build in 10 days? | First, let's calculate the total time Ben spends building the 2 rocking chairs and 1 dining chair in one day.
For the rocking chairs:
2 rocking chairs * 5 hours per rocking chair = 10 hours
For the dining chair:
1 dining chair * 3 hours per dining chair = 3 hours
Total time spent in one day:
10 hours (rocking chairs... |
the ratio of flour to water to sugar to butter in a recipe is 12 : 8 : 4 : 2. The ratio in a new recipe calls for a tripling of the ratio of flour to water and a quadrupling of the ratio of flour to sugar from the original recipe. Meanwhile, the ratio of flour to butter is doubled. If the new recipe calls for 3 cups of... | Let's first write down the original ratio of flour to water to sugar to butter, which is 12:8:4:2.
Now, according to the new recipe:
- The ratio of flour to water is tripled. The original ratio is 12:8, which simplifies to 3:2. Tripling this ratio gives us 9:2.
- The ratio of flour to sugar is quadrupled. The original... |
Tom is thrice as the age of Antonette. If their ages are 40.5 and 13.5, what is the sum of their ages? | If Tom is thrice the age of Antonette, and Antonette is 13.5 years old, then Tom is 3 times 13.5, which is 40.5 years old.
To find the sum of their ages, we add Tom's age and Antonette's age together:
40.5 (Tom's age) + 13.5 (Antonette's age) = 54
So, the sum of their ages is $\boxed{54}$ years. |
In 5 years, Raven will be 4 times as old as Phoebe. If Raven is currently 55 years old, how old is Phoebe now? | Let's denote Phoebe's current age as P.
In 5 years, Raven will be 55 + 5 = 60 years old.
According to the given information, at that time, Raven will be 4 times as old as Phoebe. So we can write the equation:
60 = 4 * (P + 5)
Now, let's solve for P:
60 = 4P + 20
Subtract 20 from both sides:
60 - 20 = 4P
40 = 4P... |
what is the square root of 400 , divided by 2 ? | The square root of 400 is 20.
When you divide 20 by 2, you get 10.
So, the square root of 400 divided by 2 is $\boxed{10}$ . |
the length of a train and that of a platform are equal . if with a speed of 36 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ? | To find the length of the train, we first need to convert the speed from kilometers per hour (km/hr) to meters per second (m/s), because the time given is in minutes.
Speed in m/s = Speed in km/hr * (1000 m / 1 km) * (1 hr / 3600 s)
Speed in m/s = 36 * (1000 / 1) * (1 / 3600)
Speed in m/s = 36 * 1000 / 3600
Speed in ... |
at a certain college , 60 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal ar... | Let's assume there are 100 students at the college for simplicity.
60% of the students are freshmen, so there are 60 freshmen.
40% of these freshmen are enrolled in the School of Liberal Arts, so there are 0.40 * 60 = 24 freshmen in the School of Liberal Arts.
20% of these freshmen in the School of Liberal Arts are... |
a line that passes through ( – 1 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ? | To find the value of k, we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Given that the slope is k, and the line passes through the points (–1, –4) and (3, k), we can plug these values into the formula:
k = (k - (-4)) / (3 - (-1))
Simplify the equation:
k = (k + 4) / (3 + 1)
k = (k + 4) / 4
Now, we can... |
A number equals some times the difference between the number and 4. The number is 5. What is the multiplier? | Let's call the number "n" and the multiplier "m". According to the given information, we have:
n = m * (n - 4)
We are given that the number n is 5. So, we can substitute n with 5 in the equation:
5 = m * (5 - 4)
Now, simplify the equation:
5 = m * 1
So, the multiplier m is:
m = 5
Therefore, the multiplier is $\... |
What is the least number which should be added to 5432 so that the sum is exactly divisible by 5, 6, 7, 11, and 13? | To find the least number that should be added to 5432 so that the sum is exactly divisible by 5, 6, 7, 11, and 13, we need to find the least common multiple (LCM) of these numbers and then find the smallest number that, when added to 5432, results in a multiple of that LCM.
First, let's find the LCM of 5, 6, 7, 11, an... |
If you had 37 bags of cookies with 19 cookies in each bag, how many cookies would you have? | To find the total number of cookies, you would multiply the number of bags by the number of cookies in each bag:
37 bags * 19 cookies/bag = 703 cookies
So, you would have $\boxed{703}$ cookies in total. |
A man buys an article for $20 and sells it for $25. What is his gain percent? | To calculate the gain percent, we need to first determine the gain amount and then divide it by the cost price, and finally multiply by 100 to get the percentage.
Gain Amount = Selling Price - Cost Price
Gain Amount = $25 - $20
Gain Amount = $5
Now, we calculate the gain percent:
Gain Percent = (Gain Amount / Cost P... |
Maddie, Luisa, and Amy counted their books. Maddie had some books. Luisa had 18 books. Together, Amy and Luisa had 9 more books than Maddie. Amy had 6 books. How many books did Maddie have? | Let's denote the number of books Maddie had as M.
According to the information given:
- Luisa had 18 books.
- Amy had 6 books.
- Together, Amy and Luisa had 9 more books than Maddie.
So, the total number of books Amy and Luisa had together is Amy's books plus Luisa's books, which is 6 + 18 = 24 books.
Since Amy and ... |
Jason spent 1/4 of his money and an additional $10 on some books. He then spent 2/5 of the remaining money and an additional $8 on some DVDs. If he was left with $130, how much money did he have at first? | Let's call the total amount of money Jason had at first "M."
After spending 1/4 of his money on books, Jason had 3/4 of his money left. Then he spent an additional $10 on books. So, the amount of money he had left after buying books is:
(3/4)M - $10
Next, Jason spent 2/5 of the remaining money on DVDs. So he spent:
... |
A train running at a certain speed crosses a pole in 9 seconds. The length of the train is 450 meters. What is the speed of the train in km/hr? | To find the speed of the train, we can use the formula:
Speed = Distance / Time
We know the distance (length of the train) is 450 meters and the time taken to cross the pole is 9 seconds.
First, we convert the distance from meters to kilometers by dividing by 1000 (since 1 km = 1000 m):
Distance in km = 450 meters ... |
A candy store sold 20 pounds of fudge for $2.50/pound, x dozen chocolate truffles for $1.50 each and 3 dozen chocolate-covered pretzels at $2.00 each. How much money did the candy store make?
If we know the answer to the above question is 212, what is the value of unknown variable x? | To determine the total revenue generated by the candy store, we need to calculate the income from each type of candy sold and then sum these amounts.
1. **Calculate the revenue from fudge:**
- The store sold 20 pounds of fudge at $2.50 per pound.
\[
\text{Revenue from fudge} = 20 \times 2.50 = 50 \text{ dolla... |
Carrie likes to buy t-shirts at the local clothing store. They cost $9.95 each. One day, she bought some t-shirts and spent $199. How many t-shirts did she buy? | To find out how many t-shirts Carrie bought, we need to divide the total amount she spent by the cost of each t-shirt.
Total spent: $199
Cost per t-shirt: $9.95
Number of t-shirts = Total spent / Cost per t-shirt
Number of t-shirts = $199 / $9.95
Number of t-shirts = 20
Carrie bought $\boxed{20}$ t-shirts. |
Solve the system of equations for x and z:
1) 19(x + y) + 17 = 19(-x + y) - 21
2) 5x - 3z = 11y - 7
Make sure to find x and z in terms of y. | Let's solve the system of equations step by step.
First, we'll solve equation 1) for x:
19(x + y) + 17 = 19(-x + y) - 21
Expanding both sides, we get:
19x + 19y + 17 = -19x + 19y - 21
Now, we'll move the terms involving x to one side and the constant terms to the other side:
19x + 19x = -21 - 17
38x = -38
Divid... |
For his car, Mike spent $235.87 on speakers, $281.45 on new tires, and $179.99 on a new steering wheel cover. He also bought a set of seat covers for $122.31 and upgraded his headlights for $98.63. Mike wanted 3 CDs for $6.29 each but decided not to. In total, Mike spent _____ on car parts. | To find the total amount Mike spent on car parts, we need to add up the costs of the speakers, tires, steering wheel cover, seat covers, and headlights. We do not include the cost of the CDs since he decided not to buy them.
Speakers: $235.87
New tires: $281.45
Steering wheel cover: $179.99
Seat covers: $122.31
Headli... |
Fran's school just instituted a school uniform policy. Each student needs to buy a certain number of complete uniforms, each consisting of pants, shirt, tie and socks. The pants cost $20, the shirt costs twice as much as the pants, the tie costs 1/5 as much as the shirt and the socks cost $3/pair. Each student needs to... | Let's calculate the cost of each item first:
- Pants cost $20.
- Shirt costs twice as much as the pants, so $20 * 2 = $40.
- Tie costs 1/5 as much as the shirt, so $40 / 5 = $8.
- Socks cost $3 per pair.
Now, let's calculate the total cost of one complete uniform:
- Pants: $20
- Shirt: $40
- Tie: $8
- Socks: $3
Tot... |
If 64 is divided by a certain number, the result is 4. What is that number? | To find the number that 64 is divided by to get 4, you can set up the equation:
64 ÷ x = 4
To solve for x, you can multiply both sides of the equation by x and then divide both sides by 4:
64 = 4x
64 ÷ 4 = x
16 = x
So the number that 64 is divided by to get 4 is $\boxed{16}$ . |
What are all the integer roots of the equation $x^3 - 3x^2 - 13x + 15 = 0$? Please enter all the integer roots, separated by commas. | To find the integer roots of the polynomial equation \(x^3 - 3x^2 - 13x + 15 = 0\), we can use the Rational Root Theorem. The Rational Root Theorem states that any potential rational root, expressed as a fraction \(\frac{p}{q}\), must have \(p\) as a factor of the constant term (here, 15) and \(q\) as a factor of the l... |
Jared wants to watch a series with four episodes. The first episode is some minutes long, the second episode is 62 minutes, the third episode is 65 minutes, and the fourth episode is 55 minutes long. The four episodes last 4 hours. How long is the first episode? | To find out how long the first episode is, we first need to determine the total number of minutes in 4 hours. Since there are 60 minutes in an hour, we multiply 4 hours by 60 minutes per hour:
4 hours * 60 minutes/hour = 240 minutes
Now we know that the total duration of the four episodes is 240 minutes. We have the ... |
If x = -5 and y = 8, what is the value of 2(x - y)^2 - xy? | First, let's substitute the values of x and y into the expression:
2(x - y)^2 - xy
2(-5 - 8)^2 - (-5)(8)
Now, let's calculate the value inside the parentheses:
-5 - 8 = -13
Now, let's square the result:
(-13)^2 = 169
Now, let's multiply this result by 2:
2 * 169 = 338
Now, let's calculate the product of x and ... |
How many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? | First, we need to convert the speed of the train from kilometers per hour (kmph) to meters per second (m/s) because the lengths given are in meters.
The conversion factor is:
1 kmph = 1000 meters / 3600 seconds
or
1 kmph = 5/18 m/s
So, the speed of the train in meters per second is:
36 kmph * (5/18) m/s/kmph = 10 m/s... |
Saleem bought 4 baskets with the average cost of $4. If Saleem also buys another basket with a certain price, the average (arithmetic mean) price of those 5 baskets is $4.8. What is the price of the fifth basket? | To find the price of the fifth basket, we first need to calculate the total cost of the first four baskets. Since the average cost of the four baskets is $4, the total cost for the four baskets is:
4 baskets * $4/basket = $16
Now, we know that when Saleem buys the fifth basket, the average cost of all five baskets be... |
If 7 < x < 9 < y < 15, then what is the possible positive integer difference of x and y with the highest value? | Given the inequality 7 < x < 9 < y < 15, we want to find the largest possible positive integer difference between x and y.
To maximize the difference between x and y, we should choose the smallest possible value for x and the largest possible value for y within the given constraints. Since x and y must be integers, we... |
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