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The ratio of boys to girls in Class A is 3 to 4. The ratio

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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio  [#permalink]

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New post 14 Nov 2016, 06:44
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changhiskhan 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

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:

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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio  [#permalink]

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New post 16 Dec 2016, 13:40
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Some great Solutions above.
Here's what i think of it now =>

The combined ratio given to us is just painfully useless.
WE can get the values of x and y from these two equations alone=>
3x=4y+1
4x=5y+2

Girls in class A => 12

Hence E

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The ratio of boys to girls in Class A is 3 to 4. The ratio  [#permalink]

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New post 24 May 2017, 06:35
Here's the simplest approach I found. First look at the new ratio 17:22 recognize that 17 is a prime number. There're only so many ways to arrive at 17.

3:4 Girls = 17
4:5 boys = 22

3x + 4y = 17--> 3*(3) = 4*(2) = 17.
Now lets try. 4*(3) + 5*(2) = 22. So that adds up.

4*3 = 12 Boys.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio  [#permalink]

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New post 17 Dec 2017, 13:52
TheGmatTutor wrote:
gurpreetsingh gives a good algebraic explanation. This question is also easy to solve by using multiples of the original ratios.

We can set up the ratios Ba (boys in A) to Ga (girls in a), and Bb (boys in b) to Gb (girls in B).

Ba/Ga = 3/4
Bb/Gb = 4/5

When combined, we'd like our final ratio ratio to be 17/22. If you write out a few multiples of each of the original ratios,

Ba/Ga = 3/4, 6/8, 9/12...
Bb/Gb = 4/5, 8/10, 12/15...

It's easy to see that by picking 9/12 for A and 8/10 for B will give you a combined ratio of 17/22. Thus, we will have 12 girls in group A.

Answer: E


TheGmatTutor how come we can add 9/12 + 8/10 without finding common denominator? I see you did (9+8)/(12+10) = 17/22. Why is this allowed?
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio &nbs [#permalink] 17 Dec 2017, 13:52

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