Question

A group of 40 kindergarten students was split into class A and class B. Class A was given 6 litres of cordial, and class B was given 5 litres of cordial. The cordial in each class was shared equally between the students in the class. The students in class A each received twice as much cordial as the students in class B. Determine the number of students in class A.

the answer is 15 btw i just want to know how to get there ​

Answer 1

Explanation:

Let's assume that there are 'x' students in class B. Then,

the number of students in class A = 40 - x

Class A was given 6 litres of cordial, which was shared equally among 40 - x students. So, each student in class A received:

6 / (40 - x)

Class B was given 5 litres of cordial, which was shared equally among x students. So, each student in class B received:

5 / x

We know that each student in class A received twice as much cordial as each student in class B. Therefore:

6 / (40 - x) = 2 × (5 / x)

Simplifying this equation, we get:

6x = 400 - 10x

Adding 10x to both sides, we get:

16x = 400

Dividing both sides by 16, we get:

x = 25

So, there are 25 students in class B, and therefore:

Number of students in class A = 40 - 25 = 15

Therefore, there are 15 students in class A.

Answer 2

15

Explanation:

Given a total of 40 students share equally 6 liters of cordial in class A and 5 liters of cordial in class B, where the students in class A get twice as much as in class B, you want to know the size of class A.

Setup

You can let 'a' represent the number of students in class A. Then the number in class B is (40 -a). The relation between the amounts of cordial that each student receives is ...

6/a = 2×5/(40 -a) . . . . . . students in A get 6/a each, twice the share in B

Solution

Multiplying by a(40 -a), we have ...

6(40 -a) = 10a

240 = 16a . . . . . . . . add 6a, simplify

a = 240/16 = 15

The number of students in class A is 15.

__

Additional comment

We like to work problems like this using ratios when possible. Here, if we halve the amount of cordial allocated to class A, then each of the 40 students receives the same amount. The ratio of cordial volumes in that case will be equal to the ratio of students

(6/2 liters) : (5 liters) = (students in class A) : (students in class B)

3 : 5 = A : B

The totals are 3+5 = 8 ratio units, and A+B = 40 students. Class A is 3/8 of the total, or ...

3/8 · 40 students = 15 students . . . . size of class A

Check: 6 liters / 15 students = 2/5 L/student. 5 liters / 25 students = 1/5 L/student, half that in class A.