BTGmoderatorDC wrote:The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
A. 8
B. 9
C. 10
D. 11
E. 12
OA E
Source: Manhattan Prep
The ratio of boys to girls in Class A is 3 to 4.
Let B = number of boys in class A
Let G = number of girls in class A
We get: B/G = 3/4
Cross multiply to get:
4B = 3G
Class A has one more boy and two more girls than class B
So B - 1 = number of boys in class B
So G - 2 = number of girls in class B
The ratio of boys to girls in Class B is 4 to 5
We get: (B - 1)/(G - 2) = 4/5
Cross multiply to get: 5(B - 1) = 4(G - 2)
Expand:
5B - 5 = 4G - 8
So, we now have the following system to solve for G:
4B = 3G
5B - 5 = 4G - 8
Take
4B = 3G and solve for B to get: B =
3G/4
Take
5B - 5 = 4G - 8 and replace B with
3G/4
We get: 5(
3G/4) - 5 = 4G - 8
Expand: 15G/4 - 5 = 4G - 8
Multiply both sides by 4 to get: 15G - 20 = 16G - 32
Solve to get: G = 12
Answer: E
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