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In a batch of 30 apples, a certain fraction are too small and 1/3 are not ripe. The others are perfect, and there are 15 perfect apples. What fraction of the apples are too small?
Marcella has 23 pairs of shoes in total, consisting of 6 different colors and 3 distinct sizes. If she loses 9 individual shoes with varying colors and sizes, what is the greatest number of matching pairs, considering both color and size, she could have left?
Justin bought some jerseys. He bought 4 long-sleeved ones that cost a certain amount each, and 2 striped ones that cost $10 each. He spent a total of $80. How much did each long-sleeved jersey cost?
Nine adults and seven children went to a play. Adult tickets are $11 each and children's tickets are $7 each. There are multiple discount options available based on the number of tickets purchased: 1. If between 10-12 tickets are purchased, a 10% discount applies to the entire purchase. 2. If between 13-15 tickets are purchased, a 15% discount applies to the entire purchase. Determine the difference between the total cost of adult tickets and children's tickets, considering the optimal discount choice.
a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 15 days before the project is completed , in how many days total will the project be completed ?
Two trains, each 100 m long, moving in opposite directions, cross each other in a certain amount of time. If one is moving twice as fast as the other, and the speed of the faster train is 24 m/s, how long does it take for the trains to cross each other?
How many moles of Potassium Nitrate are required to react with 1 mole of Sodium chloride to form 1 mole of Sodium nitrate along with 1 mole of Potassium chloride
Jose bought 20,000 square meters of land and needs to divide it equally with his four siblings. How much land, in square meters, will Jose have after dividing it with his siblings?
What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal.)
a, b, c, and d are integers. a + b + c + d < 25, a > 8, b < 5, c is an odd number, and d is an even number. What is the smallest possible value of a - b + c - d?
Xavier, Yvonne, and Zelda each try independently to solve a problem. Their individual probabilities for success are 1/4, 2/3, and 5/8, respectively. What is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . thereforedecreasing the average by 4 year . find what was theoriginal strength of class ?
The length of a room is some meters and the width is 4 m. The cost of paving the floor by slabs at the rate of Rs. 850 per sq. meter is Rs. 18,700. What is the length of the room?
a small company reduced its faculty by approximately 15 percent to 195 employees . what was the original number of employees ?
Joel collected a bin of old toys to donate. He was able to collect 18 stuffed animals, 42 action figures, 2 board games, and 13 puzzles. His sister gave him some of her old toys from her closet, and then Joel added some toys from his own closet. In all, Joel was able to donate 108 toys, and 22 of the donated toys were Joel’s. What is the ratio of the number of toys Joel added from his closet to the number of toys his sister added from hers?
Josh works 8 hours a day, a certain number of days a week, 4 weeks a month. Carl is an intern and works 2 hours less than Josh every day. Josh gets $9 an hour and Carl, half that. The company pays $1980 for the 2 together in one month. How many days a week do they work?
If 20 typists can type 40 letters in 20 minutes, then 30 typists working at the same rate can complete a certain number of letters in 1 hour. How many letters will the 30 typists complete in 1 hour?
A certain mixture of nuts consists of 5 parts almonds to some parts walnuts, by weight. There are 107.14285714285714 pounds of almonds in 150 pounds of the mixture. What is the ratio of almonds to walnuts in the mixture?
What is x if x + 2y = 100 and y = 25?
1000 men have provisions for 18 days . if 400 more men join them , for how many days will the provisions last now ?
Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at a certain speed and the second car is riding at 57 mph. They will meet 3 hours after they begin. What is the speed of the first car?
A circle graph shows how the budget of a certain company was spent: 20 percent for transportation, some percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for salaries. The area of each sector of the graph is proportional to the percent of the budget it represents. Salaries are represented by 216 degrees of the circle. What percent of the budget was spent on research and development?
Andy can get 50 demerits in a month before getting fired. In the first week, he got 2 demerits per instance for showing up late 6 times, totaling 12 demerits. In the second week, he received 15 demerits for making an inappropriate joke. He also got 3 demerits per instance for using his phone during work hours 4 times in the third week. If Andy were to get 1 demerit for not tidying up his work area for 5 days in the last week, how many more demerits could he get this month before getting fired, considering he has not received any additional demerits out of these types of incidents?
Two numbers have a certain HCF and a product of 1991. The LCM of the two numbers is 181. What is the HCF of the two numbers?
Grapes are 90% water, and when they dry, they become a certain dried fruit with a different percentage of water. A quantity of this dried fruit currently weighs 14 kilograms and weighed 116.2 kilograms when they were grapes. What is the percentage of water in the dried fruit?
If 20.5% of a class of 100 students averages 98.5% on a test, 55.5% of the class averages 76.8% on the test, and the remainder of the class averages 67.1% on the test, what is the overall class average? (Round final answer to the nearest percent).
if 12 men can reap 120 acres of land in 36 days , how many acres of land can 54 men reap in 54 days ?
Given distinct odd positive integers w, x, and z, and an expression (w^2 + x^2) * (y^2 + z^2) that has a maximum value divisible by 2, what could be the value of y?
If x is an integer such that 0 < x < 7, 0 < x < some number, 5 > x > -1, 3 > x > 0, and x + 2 < 4, then x is 1. What is the upper limit of x in the second inequality?
Teairra has 5 shirts and 24 pairs of pants in her closet. If 3 of Teairra's shirts are plaid and some of Teairra's pants are purple, she has 21 shirts and pants which are neither plaid nor purple. How many of Teairra's pants are purple?
At the zoo, there are 5 different types of animals. Seeing each animal type takes varying lengths of time: 4 minutes for the first type, 6 minutes for the second type, 7 minutes for the third type, 5 minutes for the fourth type, and 9 minutes for the fifth type. The zoo has decided to import 4 new species, with viewing times of 3, 7, 8 and 10 minutes for each species, respectively. Calculate the total time required to see all 9 animal types.
Georgia has some yellow buttons, 2 black buttons, and 3 green buttons. She gives some of the buttons to Mary, and she has 5 left. Georgia gave 4 buttons to Mary. How many yellow buttons does Georgia have?
A man can row downstream at a certain rate and upstream at 7 kmph. The man's rate in still water is 15.5 kmph and the rate of the current is 8.5 kmph. What is the man's rate when rowing downstream?
A rectangular tank needs to be coated with insulation to prevent heat loss. The dimensions of the tank are 5 feet by 10 feet by 4 feet. The insulation materials available have varying thermal resistance values (R-values) as follows: - Insulation A: R-value of 5 per inch of thickness, cost of $25 per square foot - Insulation B: R-value of 8 per inch of thickness, cost of $42 per square foot The insulation thickness must be between 2 inches and 5 inches. The overall R-value of the insulated tank should be at least R-40, and the budget for the insulation cannot exceed $12,000. Determine which insulation option, if any, meets all of these criteria. How much will it cost to cover the surface of the tank with the chosen insulation, and what will be the total R-value achieved? If both options meet the criteria, which one is the most cost-effective?
There are 8 apples in a pile on the desk. Each apple comes in a package of 11. Some apples are added to the pile, making a total of 13 apples in the pile. How many apples were added to the pile?
to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 9 hours a day ?
On the health and wellness day, fruits were distributed among the students in a school so that each student would get two bananas, one apple, and an orange. On the particular day, 420 students were absent, which resulted in the remaining students receiving four extra bananas, two more apples, and an additional orange each. Considering that bananas were distributed first, followed by apples and then oranges, find the actual number of students in the school.
A teacher had some worksheets to grade. If she graded 4, but then another 18 were turned in, she would have to grade 20 worksheets. How many worksheets did she initially have to grade?
Janet has 24 dresses. Half of them have pockets. Of those, a third have 2 pockets and the rest have 3 pockets. How many total pockets do her dresses have?
If you divide a number by ((8 ^ (2/3)) / 5) and then multiply it by the cube root of (12 ⁄ 19), followed by taking the whole expression to the power of (3/5), what is the equivalent single number you are multiplying by or dividing by?
Yolanda started walking from X to Y, a distance of 52 miles. One hour later, Bob started walking along the same road from Y to X. Bob's walking rate was 4 miles per hour. When they met, Bob had walked 28 miles. What was Yolanda's walking rate?
Set A contains all the even numbers between 42 and 90 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. Set C contains all the odd numbers between 35 and 75 inclusive. What is the result of multiplying the sum of the elements of Set B with the sum of the elements of Set C, and then dividing the product by the difference between the sum of elements of Set B and the sum of elements of Set A?
The ratio and proportion is some number : 474 :: 537 : 26. What is the first number in the ratio?
Mary's income is some percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. Mary's income is 102 percent of Juan's income. What percent more is Mary's income than Tim's income?
a plant manager must assign 8 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
A city has a population of 300,000. 50,000 people immigrate to the country and then 30,000 people leave. After that, a certain fraction of the population gets pregnant and 1/4 of those people have twins. There are 370,000 people after the births. What fraction of the population got pregnant?
If a certain pattern results in 222 being equal to a number, 333 being equal to 12, and 444 being equal to 20, what number is 222 equal to?
For Halloween Frank got ten pounds of candy and Gwen got seven pounds of candy. What is the combined weight they received?
There are 2 prime numbers between a certain number and 87 / 5. What is the lower limit of the range?
P and Q started a business investing Rs 75000 and Rs 15000 respectively. After a certain period, the profit earned is divided between P and Q in the ratio of 5:1. What is the period after which the profit is divided?
Suppose you want to buy 4 loaves of bread that cost $2.35 each, 2 jars of peanut butter that cost $3.10 each, and a jar of honey that costs $4.50. A jar of jelly is $2.85, but you don't need any jelly. You have a coupon that gives you a $2 discount on the total purchase. You have $20. How much money will you have left over?
Hannah's Vegetarian Restaurant bought some pounds of green peppers and the same amount of red peppers. They bought 0.6666666667 pounds of peppers in all. How many pounds of green peppers did they buy?
Barry and his friend, Jim, went horseback riding across central Texas. They traveled at 5 miles per hour for a certain number of hours, and then stopped for the evening. The next day, they traveled at 6 miles per hour for 6 hours, and then at half that speed for another three hours, before stopping to rest for the night. On the third and final day, they traveled for 5 hours at 7 miles per hour. In total, they traveled 115 miles during their horseback riding trip. How many hours did they travel on the first day?
There are a total of 100 jars on the shelf. Small jars hold 3 liters and large jars hold 5 liters. The jars can hold a total of 376 liters. How many small jars are on the shelf?
A company has a certain number of employees, each paid $12 per hour, working 10 hours a day, five days a week, 4 weeks a month. In August, the amount of work increased, and the company hired 200 more people. The company now pays in total $1,680,000 per month. How many employees did the company have initially?
There were 28 children riding on the bus. At the bus stop, 82 children got on the bus while some got off the bus. Then there were some children altogether on the bus. 2 more children got on the bus than those that got off. How many children were on the bus after the stop?
John is twice as old as Mary and half as old as Tonya. If Tonya is 60, what is their average age?
When positive integer x is divided by positive integer y, the remainder is 11.52. If the value of y is 95.99999999999636, what is the quotient when x is divided by y?
Barbata invests $2,400 in the national bank at 5%. She has a maximum of $7,000 to invest and wants to maximize her annual income. Apart from the national bank, she has the following investment options available: 1. International Bank - 7% interest rate, but she can only invest a maximum of $2,000. 2. Regional Bank - 10% interest rate, but she can only invest a maximum of $1,500. 3. Local Credit Union - 8% interest rate, with no maximum investment limit. How should she distribute her investments among the four options to maximize her annual income without exceeding the maximum investment amount or the specific constraints of each option?
ABCD+ABCD=5472. What is the value of D when A, B, C, and D are different numbers?
Marites internet speed is 10 megabits per second and her monthly internet bill is some amount. Marites is planning to upgrade her service and choosing between 20 Mbps and 30 Mbps. The price of the 30 Mbps is twice the amount of her current monthly bill and the price of the 20 Mbps is $10 more than her current monthly bill. She will save $120 per year if she chooses the 20 Mbps than 30 Mbps. What is her current monthly internet bill?
You have some cookies and want to share them equally with 6 people. Each person would get 4 cookies. How many cookies do you have?
We are going to draw a circle with a radius of 3 centimeters (cm) inside a square piece of paper with a side length of 30 centimeters (cm). How many circles can you draw in all?
(208% of 1265) ÷ 6 = ?
A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was some percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was 50 percent greater than its enrollment at the beginning of 1991. What was the percentage increase in enrollment from 1992 to 1993?
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 440 sq. feet, how many feet of fencing will be required?
I have purchased 5 blue apples at the store. My neighbor gives me twice as many yellow apples as I have blue ones, and then I give my son 1/5 of the total number of apples. How many apples do I have now?
if the radius of the sphere is 14 m . then its total surface area is
John's pool is some feet deeper than 2 times Sarah’s pool. John’s pool is 15 feet deep. How deep is Sarah’s pool?
Madeline has 10 flowers. If a certain number of flowers are red, 2 flowers are white, and 40% of the flowers are blue, how many flowers are red?
-200 times a certain number equals 1600. What is the number?
A certain number of scientists attended a workshop, and 16 of these were both wolf prize laureates and nobel prize laureates. Of the scientists that attended that workshop and had not received the wolf prize, the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize. 50 scientists attended that workshop, and 27 of them were nobel prize laureates. How many of the scientists were wolf prize laureates?
each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
A rectangular plot measuring 10 meters by some meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart, 24 poles will be needed. What is the length of the longer side of the rectangular plot?
Joe has 45 oranges that must be put away in boxes. Daniel comes to help and brings 16 cookies to share with Joe. There are 9 boxes. How many oranges must go in each box?
Carol and her mom were picking carrots from their garden. Carol picked 29 and her mother picked 16. If only 38 of the carrots were good, how many bad carrots did they have?
Grant decided to sell his baseball gear since he was now playing football. He sold his baseball cards for $25, his baseball bat for $10, his baseball glove at 20% off, and both pairs of his baseball cleats for $10 each. Grant made $79. What was the original price of the baseball glove before the discount?
The average weight of a certain number of persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg. The weight of the new person might be 97 kg. How many persons were there initially?
Gina's snake is an interesting creature. In the first year of its life, it eats one mouse every 4 weeks. As it grows in the second year, it starts to eat one mouse every 3 weeks. For the rest of its life, it eats a mouse every 2 weeks. Given that a non-leap year has 52 weeks and a leap year has 52 weeks and 1 day, how many mice will Gina's snake eat over a decade assuming the decade starts in a non-leap year?
Bush and Matt are brothers. Bush is younger than Matt by 3 years. This year Bush will be 12 years old. How old will Matt be a certain number of years from now if he will be 25 years old at that time?
Dave weighs some pounds and can bench press three times his body weight. Craig can only bench press 20% of the amount Dave can. Mark is new and can bench press 50 pounds less than Craig. Mark can bench press 55 pounds. How much does Dave weigh?
A train 110 m long is initially running at a speed of 60 km/hr. Its speed increases at a uniform rate of 4 km/hr^2 due to acceleration. How long does it take to completely cross a bridge that is 330 m in length?
13 campers went rowing and 59 campers went hiking in the morning. Some campers went rowing in the afternoon. In all, 34 campers went rowing. How many campers went rowing in the afternoon?
If to a certain number, 720 is added, and the sum is divided by 125, the quotient will be equal to a value divided by 462. The number is 1280. What is the value in the numerator?
If f(x) = 2x^2 + y, and f(2) = 20, what is the value of f(5)?
The Indigo Restaurant receives 18 online customer reviews. They receive six 5-star reviews, seven 4-star reviews, four 3-star reviews, and one 2-star review. What is the average star rating for Indigo Restaurant based on these reviews?
Josh is saving up for a box of cookies. To raise the money, he is going to make bracelets and sell them. It costs $1 for supplies for each bracelet and he sells each one for $1.5. He made 12 bracelets and after buying the cookies still has $3. How much did the box of cookies cost?
Out of 500 customers surveyed at a fashion store, they were divided into three spending ranges: less than $100, $100-$200, and above $200. The customers were also asked whether they purchased casual or formal clothing, and they reported their overall satisfaction level. The survey results are as follows: 1. 50% of the customers purchased clothes for less than $100; 30% spent between $100-$200, and the remaining 20% spent above $200. 2. 60% of customers bought casual clothing, while 40% bought formal clothing. 3. For customers who spent less than $100: 45% were overall satisfied, and 65% of them purchased casual clothing. 4. For customers who spent between $100-$200: 35% reported satisfaction, and 50% of them bought casual clothing. 5. Among customers who spent above $200, only 20% were overall satisfied, and only 40% purchased casual clothing. What percentage of customers purchased formal clothes for at least $100 and reported overall dissatisfaction?
Jonah bought 6 pineapples for $3 each. Each pineapple could be cut into 12 pineapple rings. He sold 4 pineapple rings for $5 each. How much profit did Jonah make?
Mark has an egg farm. His farm supplies one store with some dozen eggs and another store with 30 eggs each day. He supplies these two stores with 630 eggs in a week. How many dozen eggs does he supply to the first store each day?
To pave a rectangular courtyard 40 m long and 16 1/2 m wide, 132 paving stones, each measuring a certain length * 2 m, are required. What is the length of each paving stone?
Olivia was making baggies of cookies with 9 cookies in each bag. If she had 13 chocolate chip cookies and 41 oatmeal cookies, how many baggies could she make?
how many hours are there in 660 minutes ?
at what rate percent on simple interest will rs . 750 amount to rs . 900 in 8 years ?
A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, some percent for supplies, and the remainder for transportation. The area of each sector of the graph is proportional to the percent of the budget it represents. 72 degrees of the circle are used to represent transportation. What percent of the budget was spent on supplies?
Andy, a part of the recycling team, decided to gather tin foil wrappers. He was able to pick up 34 wrappers around the village dumpster. His best friend Max collected 15 wrappers, their other friend Zoe collected 25 wrappers, and a fourth friend, Mia, collected 19 wrappers. How many wrappers were gathered in total by all four friends?
in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 11 , 0 ) , ( 0 , - 3.5 ) , ( - 11 , 0 ) ?
the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 32 of the dish ?
what is the smallest integer c for which 27 ^ c > 3 ^ 24 ?