M7MBA wrote: ↑Sun Sep 26, 2021 11:52 am
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
Answer:
E
Source: Manhattan GMAT
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
