The ratio of the number of boys to the number of girls in Group A was 4:1
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
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
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 ...
Certainly! Let's break down the given information to find the answers to both parts of the question.
a) To find the ratio of the number of boys in Group A to the number of boys in Group B, we need to know the total number of boys in each group.
Let's assume the number of boys in Group A is represented by the variable 'x'. Since the ratio of the number of boys to girls in Group A is 4:1, it means that for every 4 boys, there is 1 girl. So, the number of girls in Group A would be (1/4) * x.
Similarly, let's assume the number of boys in Group B is represented by the variable 'y'. Since the ratio of the number of boys to girls in Group B is 2:3, it means that for every 2 boys, there are 3 girls. So, the number of girls in Group B would be (3/2) * y.
Given that there were twice as many children in Group A as in Group B, we can set up an equation:
Number of children in Group A = 2 * Number of children in Group B
Number of children in Group A = (Number of boys in Group A) + (Number of girls in Group A)
Number of children in Group B = (Number of boys in Group B) + (Number of girls in Group B)
Plugging in the values we derived earlier, we can rewrite the equation as:
x + (1/4) * x = 2 * [(y) + (3/2) * y]
Simplifying this equation will help us find the ratio of the number of boys in Group A to the number of boys in Group B.
b) To find the number of children in Group A, we need to use the additional information provided after 10 boys and 10 girls left Group B. Let the variables 'x' and 'y' represent the number of boys and girls, respectively, in the new situation.
Since the ratio of boys in Group B to the girls in Group B became 1:2, it means that for every 1 boy, there are 2 girls. So, we can write an equation based on the new situation:
New ratio of boys in Group B: New ratio of girls in Group B = 1:2
This can be written as (x-10)/(y-10) = 1/2
Using this equation, along with the information derived earlier, we can find the number of children in Group A.
I hope this explanation helps! Let me know if you have any further questions.