The ratio of the number of boys to the number of girls in Group A was 4:1

Question

The ratio of the number of boys to the number of girls in group B was 2: 3
There were twice as many children in Group A as in Group B

a) What was the ratio of the number of boys in Group A to the number of boys in Group B?

b) 10 boys and 10 girls left in Group B, The ratio of the number of boys in Group B to the number of girls in Group B became 1:2. How many children were there in Group A?

Could you please help? Thanks very much

Answer 1

let 2x be the number of boys in B
Then there are 3x girls in B
That means there are 10x children in group A, with
8x boys
2x girls
Aboys : Bboys = 8x:2x = 4:1

see what you can do with part B ...

Answer 2

A: boys : girls = 4x : x
B: boys : girls = 2y : 3y

4x+x = 2(2y+3y)
5x = 10y
x = 2y

boysA : boysB = 4x :2y = 8y:2y = 4:1

b) 2y-10 : 3y-10 = 1 : 2
(2y-10)/(3y-10) = 1/2
4y - 20 = 3y - 10
y = 10
then since x = 2y, x = 20
and total is A is 5x = 100