## 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 $$5$$

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### 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 $$5$$

by Gmat_mission » Fri Jan 28, 2022 11:58 am

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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

Source: Manhattan GMAT

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### Re: 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 \

by [email protected] » Sun Jan 30, 2022 6:27 am
Gmat_mission wrote:
Fri Jan 28, 2022 11:58 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

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

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### Re: 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 \

by GMATGuruNY » Tue Feb 01, 2022 11:46 am
Gmat_mission wrote:
Fri Jan 28, 2022 11:58 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
We can PLUG IN THE ANSWERS, which represent the number of girls in Class A.
In Class A, the ratio of boys to girls is 3 to 4, implying that the number of girls in Class A must be a MULTIPLE OF 4.
Eliminate B, C and D.

Answer choice A: 8 girls in Class A
In this case:
Since the ratio of boys to girls in Class A = 3:4 = 6:8, Class A has 6 boys and 8 girls.
Since Class B has one less boy and two fewer girls, Class B has 5 boys and 6 girls.
Doesn't work:
In Class B, the ratio of boys to girls must be 4 to 5.
Eliminate A.