There are 75% fewer boys than girls in Club A. The ratio of the number of boys to the number of girls in Club B is 3 : 8. There is an equal number of boys in Club A and Club B. If Club A has 36 more girls than Club B, how many boys are there in Club A?

club A:

number of girls ---- 4x
number of boys ----- x

club B:
number of girls ---- 8y
number of boys ----- 3y

"There is an equal number of boys in Club A and Club B"
---> x = 3y
"Club A has 36 more girls than Club B"
---> 4x - 8y = 36 or x - 2y = 9

solve the two equations in x and y.
I would use substitution.

To solve this problem, let's break it down step by step.

Step 1: Find the number of boys and girls in Club B.
- Let's assume the number of boys in Club B is 3x (since the ratio is 3:8).
- The number of girls in Club B would then be 8x.

Step 2: Use the information given in the problem to set up equations.
- Since Club A has 75% fewer boys than girls, we can calculate the ratio of boys to girls as 1:4 (since 100% - 75% = 25%, which is equivalent to 1:4).
- Let's assume the number of boys in Club A is y. Then the number of girls in Club A would be 4y.

Step 3: Set up an equation using the given information that there is an equal number of boys in both clubs.
- We know that y (number of boys in Club A) is equal to 3x (number of boys in Club B).
- This gives us the equation: y = 3x.

Step 4: Set up another equation using the given information that Club A has 36 more girls than Club B.
- We know that 4y (number of girls in Club A) is equal to 8x (number of girls in Club B) plus 36.
- This gives us the equation: 4y = 8x + 36.

Step 5: Solve the system of equations.
- Substitute the value of y from the first equation into the second equation: 4(3x) = 8x + 36.
- Simplify: 12x = 8x + 36.
- Subtract 8x from both sides: 4x = 36.
- Divide both sides by 4: x = 9.

Step 6: Find the number of boys in Club A.
- Using the value of x, substitute it into the equation y = 3x: y = 3(9).
- Calculate: y = 27.

Therefore, there are 27 boys in Club A.