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<s>[INST] An amount of money is to be divided between p, q, and r in the ratio of 3 : 7 : 12. The difference between the shares of p and q is Rs. 3200. What will be the difference between q and r's share? [/INST] Let's denote the common multiple of the ratio as x. So, the shares of p, q, and r will be 3x, 7x, and 12x r... |
<s>[INST] an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3200 , what will be the difference between q and r ' s share ? [/INST] Let's denote the shares of p, q, and r as 3x, 7x, and 12x respectively, where x is the common mult... |
<s>[INST] An amount of money is to be divided between p, q, and r in the ratio of 3 : 7 : 12. The difference between the shares of p and q is some amount, and the difference between q and r's share is Rs. 4000. What is the difference between the shares of p and q? [/INST] Let's denote the common multiple of the ratio a... |
<s>[INST] If 5 - 5 / x = 4 + 4 / x, what is the value of x? [/INST] To find the value of x, we can start by solving the equation:
5 - 5/x = 4 + 4/x
First, let's get rid of the fractions by multiplying both sides of the equation by x:
x(5 - 5/x) = x(4 + 4/x)
This simplifies to:
5x - 5 = 4x + 4
Now, let's move the ... |
<s>[INST] if 5 - 5 / x = 4 + 4 / x , then x = [/INST] To solve for x, we can start by combining like terms on both sides of the equation.
Given: 5 - 5/x = 4 + 4/x
First, let's get rid of the fractions by multiplying every term by x to eliminate the denominators:
x(5) - x(5/x) = x(4) + x(4/x)
This simplifies to:
5... |
<s>[INST] which digits should come in place of * and $ if the number 62684 * $ is divisible by both 8 and 5 ? [/INST] For a number to be divisible by 5, its last digit must be either 0 or 5. Since we have a $ symbol in the place of the last digit, $ must be either 0 or 5 for the number to be divisible by 5.
For a numb... |
<s>[INST] Which digits should come in place of * and $ if the number 62684 * $ is divisible by 8 and a certain number, and the digits are * = 4 and $ = 0? What is that certain number? [/INST] For a number to be divisible by 8, the last three digits of the number must be divisible by 8. In the number 62684*$, the last t... |
<s>[INST] Which digit should come in place of $ if the number 62684 4 $ is divisible by both 8 and 5? [/INST] For a number to be divisible by 5, its last digit must be either 0 or 5. Since we are looking for a single digit to replace the $, the only options are 0 or 5.
For a number to be divisible by 8, the last three... |
<s>[INST] a gardener wants to plant trees in his garden in rows in such away that the number of trees in each row to be the same . if there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row ? [/INST] If there are 24 rows with 42 trees in each row, the total... |
<s>[INST] If 5 - 5 / x = some number plus 4 / x, and x = 9, what is the number? [/INST] Let's first solve the equation for the unknown number. We have:
5 - 5/x = number + 4/x
To find the number, we need to isolate it on one side of the equation. Let's move the terms involving x to one side and the constant terms to t... |
<s>[INST] Which digits should come in place of * and $ if the number 62684 * $ is divisible by a certain number and 5, and the digits are * = 4 and $ = 0? What is that certain number? [/INST] To be divisible by 5, a number must end in either 0 or 5. Since we are given that $ = 0, the number 62684*0 is already divisible... |
<s>[INST] A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row is the same. If there are 24 rows, the number of trees in each row is 42. If there are 12 more rows, how many trees are in each of these additional rows? [/INST] If there are 24 rows with 42 trees in each ... |
<s>[INST] Which digit should come in place of * if the number 62684 * 0 is divisible by both 8 and 5? [/INST] For a number to be divisible by 5, its last digit must be either 0 or 5. Since the number already ends with a 0, this condition is satisfied.
For a number to be divisible by 8, the last three digits of the num... |
<s>[INST] If some number minus 5 / x = 4 + 4 / x, and x = 9, what is the number? [/INST] Let's call the number we're looking for "N". According to the equation given:
N - 5/x = 4 + 4/x
We are given that x = 9, so let's substitute 9 for x in the equation:
N - 5/9 = 4 + 4/9
To solve for N, we need to isolate it on on... |
<s>[INST] A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row is the same. If there are 24 rows, the number of trees in each row is a certain number. If there are 12 more rows, the number of trees in each row is 28. How many trees are in each row initially? [/INST] L... |
<s>[INST] A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row is the same. If there are a certain number of rows, the number of trees in each row is 42. If there are 12 more rows, the number of trees in each row is 28. How many rows are there initially? [/INST] Let's... |
<s>[INST] A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row is the same. If there are 24 rows, the number of trees in each row is 42. If there are a certain number of additional rows, the number of trees in each row is 28. How many additional rows are there? [/INST... |
<s>[INST] An amount of money is to be divided between p, q, and r. The difference between the shares of p and q is Rs. 3200, and the difference between q and r's share is Rs. 4000. What is the ratio of their shares? [/INST] Let's denote the shares of p, q, and r as P, Q, and R respectively.
According to the problem, w... |
<s>[INST] The cash realized on selling a 14% stock is Rs. 107.25. The total amount before brokerage is Rs. 107. What is the percentage of the brokerage? [/INST] To find the percentage of the brokerage, we need to calculate the difference between the total amount before brokerage and the cash realized on selling the sto... |
<s>[INST] In a race where 16 cars are running, the chance that car X will win is 1/4, that Y will win is 1/12, and that Z will win is some probability. Assuming that a dead heat is impossible, the chance that one of them will win is 0.47619047619047616. What is the probability that car Z will win? [/INST] Let's denote ... |
<s>[INST] The cash realized on selling a 14% stock is a certain amount, with the brokerage being 1/4%. The total amount before brokerage is Rs. 107. What is the cash realized on selling the stock? [/INST] To find the cash realized on selling the stock, we first need to calculate the brokerage fee and then subtract it f... |
<s>[INST] In a race where 16 cars are running, the chance that car X will win is 1/4, that Y will win is some probability, and that Z will win is 1/7. Assuming that a dead heat is impossible, the chance that one of them will win is 0.47619047619047616. What is the probability that car Y will win? [/INST] Let's denote t... |
<s>[INST] In a race where 16 cars are running, the chance that car X will win is 1/4, that Y will win is 1/12, and that Z will win is 1/7. Assuming that a dead heat is impossible, find the chance that one of them will win. [/INST] To find the chance that one of the cars X, Y, or Z will win, we can add their individual ... |
<s>[INST] in a race where 16 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 12 and that z will win is 1 / 7 . assuming that a dead heat is impossible , find the chance that one of them will win . [/INST] To find the probability that one of the three cars (X, Y, or Z) will win, we ca... |
<s>[INST] In a race where 16 cars are running, the chance that car X will win is some probability, that Y will win is 1/12, and that Z will win is 1/7. Assuming that a dead heat is impossible, the chance that one of them will win is 0.47619047619047616. What is the probability that car X will win? [/INST] Let's denote ... |
<s>[INST] the cash realised on selling a 14 % stock is rs . 107.25 , brokerage being 1 / 4 % is ? [/INST] To calculate the brokerage on the sale of a 14% stock, we need to know the total amount for which the stock was sold. Since the cash realized is Rs. 107.25, this is the amount after the brokerage has been deducted.... |
<s>[INST] The cash realized on selling a certain percentage stock is Rs. 107.25, with the brokerage being 1/4%. The total amount before brokerage is Rs. 107. What is the percentage of the stock? [/INST] Let's denote the percentage of the stock sold as P%.
The brokerage is 1/4%, which means that for every 100 Rs of the... |
<s>[INST] The cash realized on selling a 14% stock is Rs. 107.25, with the brokerage being 1/4%. What is the total amount before brokerage? [/INST] To find the total amount before brokerage, we need to calculate the amount that was realized after deducting the brokerage fee.
Let's denote the total amount before broker... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x < 18, 13 > x > 2, x < 12, and x + 1 < 13, and x is greater than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one to find the range of possible values for x:
1. \(5 < x < 21\): This means x can be any integer from 6 to ... |
<s>[INST] If x is an integer such that x < 21, 7 < x < 18, 13 > x > 2, 12 > x > 9, and x + 1 < 13, and x is greater than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one:
1. x < 21: This tells us that x is less than 21, but it doesn't give us a lower bound.
2. 7 < x < 18: Th... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x < 18, x < 13, 12 > x > 9, and x + 1 < 13, and x is greater than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one to find the range of possible values for x:
1. \(5 < x < 21\): x is greater than 5 and less than 21.
2. \... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x < 18, 13 > x > 2, 12 > x > 9, and x is increased by a certain number to be less than 13, what is that number? [/INST] Let's first find the range of x that satisfies all the given conditions:
1. \(5 < x < 21\)
2. \(7 < x < 18\)
3. \(13 > x > 2\)
4. \(12 > x > 9\)... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x < 18, 13 > x > 2, 12 > x > 9, and x + 1 < 13, what is the value of x? [/INST] Let's analyze the given inequalities one by one and find the common range for x:
1. \(5 < x < 21\): x is greater than 5 and less than 21.
2. \(7 < x < 18\): x is greater than 7 and les... |
<s>[INST] If x is an integer such that 5 < x, 7 < x < 18, 13 > x > 2, 12 > x > 9, and x + 1 < 13, and x is less than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one:
1. \( 5 < x \) means x is greater than 5.
2. \( 7 < x < 18 \) means x is greater than 7 and less than 18.
3.... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x < 18, 13 > x > 2, x > 9, and x + 1 < 13, and x is less than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one to find the range of possible values for x:
1. \(5 < x < 21\): x is greater than 5 and less than 21.
2. \(7 <... |
<s>[INST] Set A contains all the even numbers between 10 and 50 inclusive. Set B contains all the even numbers between 110 and 150 inclusive. What is the difference between the sum of elements of Set B and the sum of the elements of Set A? [/INST] To find the sum of the elements in each set, we can use the formula for ... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x, 13 > x > 2, 12 > x > 9, and x + 1 < 13, and x is less than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one:
1. \(5 < x < 21\): This means x is greater than 5 and less than 21.
2. \(7 < x\): This means x is greater th... |
<s>[INST] set a contains all the even numbers between 10 and 50 inclusive . set b contains all the even numbers between 110 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ? [/INST] To find the sum of the elements in each set, we can use the formula f... |
<s>[INST] If x is an integer such that 5 < x < 21, 7 < x < 18, x > 2, 12 > x > 9, and x + 1 is less than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one to find the range of possible values for x:
1. \(5 < x < 21\): x is greater than 5 and less than 21.
2. \(7 < x < 18\): x... |
<s>[INST] if x is an integer such that 5 < x < 21 , 7 < x < 18 , 13 > x > 2 , 12 > x > 9 , and x + 1 < 13 , then x is [/INST] To find the value of x, we need to consider all the given inequalities and find the common range that satisfies all of them.
1. \(5 < x < 21\)
2. \(7 < x < 18\)
3. \(13 > x > 2\)
4. \(12 > x > ... |
<s>[INST] If x is an integer such that 5 < x < 21, x < 18, 13 > x > 2, 12 > x > 9, and x + 1 < 13, and x is greater than a certain number, what is that number? [/INST] Let's analyze the given conditions one by one:
1. \(5 < x < 21\): This means x is greater than 5 and less than 21.
2. \(x < 18\): This means x is less ... |
<s>[INST] The h.c.f of 136, 144, and a third number is a certain number, and their l.c.m is 2^4 * 3^2 * 17 * 7. The third number is 168. What is the h.c.f of the three numbers? [/INST] To find the highest common factor (h.c.f) of the three numbers 136, 144, and 168, we need to find the common prime factors of these num... |
<s>[INST] At Deluxe Paint Store, fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint. How many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint? [/INST] First, let's determine th... |
<s>[INST] h . c . f of 136 , 144 and a third number is 8 and their l . c . m is 2 ^ 4 * 3 ^ 2 * 17 * 7 . the third number is : [/INST] To find the third number, we need to use the relationship between the highest common factor (HCF) and the least common multiple (LCM) of three numbers. The product of the HCF and LCM of... |
<s>[INST] The h.c.f of 136, 144, and a third number is 8, and their l.c.m is a certain number. The third number is 168. What is the l.c.m of the three numbers? [/INST] To find the least common multiple (LCM) of the three numbers 136, 144, and 168, we can use the relationship between the highest common factor (HCF) and ... |
<s>[INST] The h.c.f of 136, 144, and a third number is 8, and their l.c.m is 2^4 * 3^2 * 17 * 7. What is the third number? [/INST] To find the third number, we need to use the relationship between the highest common factor (HCF) and the least common multiple (LCM) of three numbers. The product of the HCF and LCM of thr... |
<s>[INST] If n = ( 33 ) ^ some power + ( 43 ) ^ 32, the units digit of n is 2. What is the exponent of the first term in the equation? [/INST] To find the units digit of n, we need to consider the units digit of each term separately.
The units digit of any power of 43 will be the same as the units digit of 3 raised to... |
<s>[INST] If n = ( 33 ) ^ 43 + ( 43 ) ^ 32, what is the units digit of n? [/INST] To find the units digit of n, we only need to consider the units digits of the numbers being raised to powers and how they behave when exponentiated.
For the first term (33)^43, the units digit of 33 is 3. The pattern of the units digit ... |
<s>[INST] What is the smallest number which, when diminished by 20, is divisible by 15, 30, some number, and 60? The answer is 200. What is the third number in the list of divisors? [/INST] Let's call the third number \( x \). We are looking for the smallest number which, when diminished by 20, is divisible by 15, 30, ... |
<s>[INST] What is the smallest number which, when diminished by 20, is divisible by some number, 30, 45, and 60? The answer is 200. What is the first number in the list of divisors? [/INST] To find the smallest number which, when diminished by 20, is divisible by some number, 30, 45, and 60, we need to find the least c... |
<s>[INST] if n = ( 33 ) ^ 43 + ( 43 ) ^ 32 what is the units digit of n ? [/INST] To find the units digit of \( n \), we only need to consider the units digits of the two terms being added together.
For the first term, \( (33)^{43} \), the units digit of 33 is 3. We need to find the pattern of the units digit when 3 i... |
<s>[INST] What is the smallest number which, when diminished by 20, is divisible by 15, 30, 45, and 60? [/INST] To find the smallest number that meets the given conditions, we need to find the least common multiple (LCM) of the divisors 15, 30, 45, and 60. The LCM of a set of numbers is the smallest number that is divi... |
<s>[INST] what is the smallest number which when diminished by 20 , is divisible 15 , 30 , 45 and 60 ? [/INST] To find the smallest number that meets the given conditions, we need to find the least common multiple (LCM) of the divisors 15, 30, 45, and 60. The LCM of these numbers is the smallest number that is divisibl... |
<s>[INST] Joe has a total of $200 in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. Now, he has a certain amount of money in each pocket, and originally, he had $160 in his left pocket. What is... |
<s>[INST] What is the smallest number which, when diminished by 20, is divisible by 15, 30, 45, and some number? The answer is 200. What is the fourth number in the list of divisors? [/INST] Let's find the smallest number that meets the given conditions. We know that the number, when diminished by 20, is divisible by 1... |
<s>[INST] the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 60 per cent . the two reductions together are equal to a single reduction of [/INST] Let's assume the original price of the cycle is P.
After the first reduction of 25%, the new price becomes:
P - (25/100 * P) = P - 0.25P ... |
<s>[INST] Joe has a total of $200 in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes some amount from his left pocket and puts it in his right pocket. Now, he has an equal amount of money in each pocket, and originally, he had $160 in his left pocket. ... |
<s>[INST] Find a number which, when diminished by some value, is divisible by 15, 30, 45, and 60. The smallest such number is 200. What is the value that needs to be diminished? [/INST] To find a number that is divisible by 15, 30, 45, and 60, we need to find the least common multiple (LCM) of these numbers. The LCM of... |
<s>[INST] joe has a total of $ 200 in his two pockets . he takes one fourth of the money in his left pocket and puts it in his right pocket . he then takes $ 20 from his left pocket and puts it in his right pocket . if he now has an equal amount of money in each pocket , then how much money did he originally have in hi... |
<s>[INST] The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 60 per cent. What is the single percentage reduction equivalent to these two reductions together? [/INST] Let's assume the original price of the cycle is $P$.
After the first reduction of 25%, the new price becomes:
$P - 0.... |
<s>[INST] Joe has a total of some amount in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. Now, he has an equal amount of money in each pocket, and originally, he had $160 in his left pocket. W... |
<s>[INST] Given a number, there is an algorithm described here to find its sum and number of factors. For example, let us take the number 1225. What is the sum and number of factors for this number? [/INST] To find the sum and number of factors of a given number, we need to first find all the factors of the number. A f... |
<s>[INST] Joe has a total of $200 in his two pockets. He takes some fraction of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. Now, he has an equal amount of money in each pocket, and originally, he had $160 in his left pocket. What ... |
<s>[INST] The price of a cycle is reduced by some percentage. The new price is reduced by a further 60 per cent. The two reductions together are equal to a single reduction of 70 per cent. What is the first percentage reduction? [/INST] Let's denote the original price of the cycle as P and the first percentage reductio... |
<s>[INST] The price of a cycle is reduced by 25 per cent. The new price is reduced by a further percentage. The two reductions together are equal to a single reduction of 70 per cent. What is the second percentage reduction? [/INST] Let's assume the original price of the cycle is $P$.
After the first reduction of 25%,... |
<s>[INST] Given a number, there is an algorithm described here to find its sum and number of factors. The sum and number of factors for a certain number is 1767. What is the number? [/INST] To find the number given its sum and number of factors, we need to understand the properties of factors of a number. The sum of fa... |
<s>[INST] if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 9 have ? [/INST] To find the number of divisors of a number, we can use the formula that applies to numbers expressed in their prime factorization form:
If a number N can be expressed as N = p1^a * p2^b * ... * pk^k, where p1, p2, ... |
<s>[INST] If p and q are prime numbers, the product of p raised to a certain power and q raised to the power of 9 has 50 divisors. What is the certain power? [/INST] Let's denote the certain power of p as x. The product of p raised to the power of x and q raised to the power of 9 can be written as p^x * q^9.
The numbe... |
<s>[INST] If p and q are prime numbers, how many divisors does the product p ^ 4 * q ^ 9 have? [/INST] To find the number of divisors of a number, we can use the formula that applies to numbers expressed in their prime factorization form:
If a number N can be expressed as N = p1^a * p2^b * ... * pk^k, where p1, p2, ..... |
<s>[INST] If p and q are prime numbers, the product of p raised to the power of 4 and q raised to a certain power has 50 divisors. What is the certain power? [/INST] The number of divisors of a number can be found using its prime factorization. If a number \( n \) has a prime factorization of \( n = p_1^{a_1} \cdot p_2... |
<s>[INST] If a - b = 3 and a^2 + b^2 = 29, find the value of ab? [/INST] To find the value of ab, we can use the given equations:
1) a - b = 3
2) a^2 + b^2 = 29
We can square the first equation to get a new equation that includes the term ab:
(a - b)^2 = 3^2
a^2 - 2ab + b^2 = 9
Now we have two equations:
3) a^2 - ... |
<s>[INST] If a certain prime number and q are prime numbers, the product of the certain prime number raised to the power of 4 and q raised to the power of 9 has 50 divisors. What is the certain prime number? [/INST] Let's denote the certain prime number as p. The product of p raised to the power of 4 and q raised to th... |
<s>[INST] if a - b = 3 and a 2 + b 2 = 29 , find the value of ab ? [/INST] To find the value of \( ab \), we can use the given equations:
1) \( a - b = 3 \)
2) \( a^2 + b^2 = 29 \)
We can square the first equation to get a new equation involving \( a^2 \), \( b^2 \), and \( ab \):
\( (a - b)^2 = 3^2 \)
\( a^2 - 2ab ... |
<s>[INST] given a number , there is an algorithm described here to find it ' s sum and number of factors . for example , let us take the number 1225 ? [/INST] To find the sum and number of factors of a given number, such as 1225, you can follow these steps:
1. **Prime Factorization**: First, find the prime factorizati... |
<s>[INST] If p and a certain prime number are prime numbers, the product of p raised to the power of 4 and the certain prime number raised to the power of 9 has 50 divisors. What is the certain prime number? [/INST] Let's denote the certain prime number as q. The product of p raised to the power of 4 and q raised to th... |
<s>[INST] In a 3 x 3 matrix, the elements in the first row are (v, 50, w), the second row (196, x, y), and the third row (269, z, 123). It is given that the sum of the numbers in each row, column, diagonal are the same. What is the value of (y + z)? [/INST] Let's denote the sum of the numbers in each row, column, and d... |
<s>[INST] A bag contains an equal number of one rupee, 50 paise, and 25 paise coins respectively. If the total value is 140, how many coins of each type are there? [/INST] Let's assume the number of coins of each type is x.
Since there are equal numbers of one rupee, 50 paise, and 25 paise coins, we have:
- x coins of... |
<s>[INST] A bag contains an equal number of one rupee, 50 paise, and 25 paise coins respectively. If there are 80 coins of each type, what is the total value of the coins in the bag? [/INST] To find the total value of the coins in the bag, we need to calculate the value of each type of coin and then sum them up.
1. On... |
<s>[INST] A bag contains some coins of one rupee, 50 paise, and 25 paise. The total value is 140. There are 80 coins of each type. What is the ratio of the number of one rupee coins to the number of 50 paise coins and 25 paise coins? [/INST] Since there are 80 coins of each type, we can calculate the total value of eac... |
<s>[INST] a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 140 , how many coins of each type are there ? [/INST] Let's assume the number of coins of each type is x.
Since there are equal numbers of one rupee, 50 paise, and 25 paise coins, we have:
Total va... |
<s>[INST] A certain volume of a solution of salt and water is 10% salt. 20 gallons of water must be added to the solution in order to decrease the salt to 8% of the volume. What is the initial volume of the solution? [/INST] Let's denote the initial volume of the solution as V gallons. Since the solution is 10% salt, t... |
<s>[INST] An 80-gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume? [/INST] Let's first determine the amount of salt in the original 80-gallon solution. Since the solution is 10% salt, we can calculate the amount of sa... |
<s>[INST] An 80-gallon solution of salt and water has a certain percentage of salt. 20 gallons of water must be added to the solution in order to decrease the salt to 8% of the volume. What is the initial percentage of salt in the solution? [/INST] Let's denote the initial percentage of salt in the solution as P%. This... |
<s>[INST] An 80-gallon solution of salt and water is 10% salt. A certain amount of water must be added to the solution in order to decrease the salt to a specific percentage of the volume. If 20 gallons of water are added, what is the new percentage of salt in the solution? [/INST] To find the new percentage of salt in... |
<s>[INST] The average height of 35 boys in a class was calculated as 184 cm. It was later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (round off your answer to two decimal places)? [/INS... |
<s>[INST] Jennifer had $90 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? [/INST] First, let's calculate how much Jennifer spent on each item:
1. Sandwich: 1/5 of $90 = $90 / 5 = $18
2. Museum ticket: 1/... |
<s>[INST] the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ? [/... |
<s>[INST] a 80 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ? [/INST] Let's denote the amount of water to be added as \( x \) gallons.
The initial amount of salt in the 80-gallon solution is 10% of 80 gallons... |
<s>[INST] jennifer had $ 90 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ? [/INST] Let's calculate how much Jennifer spent on each item:
1. Sandwich: 1/5 of $90 = $90 * (1/5) = $18
2. Museum t... |
<s>[INST] Jennifer had $90 to spend on herself. She spent a fraction of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. Jennifer has $12 left over. What fraction of her money did she spend on the sandwich? [/INST] Let's denote the fraction of money Jennifer spent on the sandwich as \( x ... |
<s>[INST] Jennifer had $90 to spend on herself. She spent 1/5 of the money on a sandwich, a fraction for a ticket to a museum, and 1/2 of it on a book. Jennifer has $12 left over. What fraction of her money did she spend on the museum ticket? [/INST] Let's start by calculating how much money Jennifer spent in total bef... |
<s>[INST] Jennifer had $90 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and a fraction of it on a book. Jennifer has $12 left over. What fraction of her money did she spend on the book? [/INST] Let's calculate the amount Jennifer spent on the sandwich and the museum ticke... |
<s>[INST] find large number from below question the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder [/INST] Let's call the larger number L and the smaller number S.
According to the problem, the difference between the larger number and the... |
<s>[INST] Jennifer had some money to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. Jennifer has $12 left over. How much money did Jennifer initially have to spend on herself? [/INST] Let's denote the initial amount of money Jennifer had as \( M \).
A... |
<s>[INST] The difference of two numbers is a certain value. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. The larger number is 1584. What is the difference between the two numbers? [/INST] Let's denote the larger number as L and the smaller number as S.
According to the proble... |
<s>[INST] The difference of two numbers is 1335. On dividing the larger number by the smaller, we get 6 as quotient and a certain remainder. The larger number is 1584. What is the remainder when the larger number is divided by the smaller number? [/INST] Let's call the smaller number "x". The larger number is given as ... |
<s>[INST] what is the product of all the possible values of x if x ^ 2 - 9 x + 20 ? [/INST] To find the product of all possible values of x for the quadratic equation x^2 - 9x + 20, we first need to find the roots of the equation. We can do this by factoring the quadratic equation.
The equation x^2 - 9x + 20 can be fa... |
<s>[INST] In a group of ducks and cows, the total number of legs are some more than twice the number of heads. There are 18 buffaloes. How many more legs are there than twice the number of heads? [/INST] Let's denote the number of ducks as D and the number of cows as C. Each duck has 2 legs and each cow has 4 legs. Buf... |
<s>[INST] In a group of ducks and cows, the total number of legs are 36 more than twice the number of heads. Find the total number of buffaloes. [/INST] It seems there might be a confusion in the question. You mentioned ducks and cows in the group, but then asked for the total number of buffaloes. I will assume you mea... |
<s>[INST] The difference of two numbers is 1335. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the larger number? [/INST] Let's call the larger number L and the smaller number S.
According to the problem, the difference between the larger and smaller number is 1335:
L ... |
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