Problem Solving

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 the number of boys in Class B is one less than the number of boys in Class A, and if the number of girls in Class B is two less than the number of girls in Class A, how many girls are in Class A?

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12

I got answer without using the ratio 17:22.

4y = 3x -1
5y = 4x -2

solve and answer. please validate my method.

Class A: B/G=3/4

Class B: b/g=4/5

B+b/G+g=17/22

b=B-1

g=G-2

2B-1/2G-2=17/22

4B=3G

2B=3G/2

3G/2-1/2G-2=17/22

33G-22=34G-34

G=12

E

I don't really understand the method that you used.

OA???
IMO 12
I did it in 45 sec. By getting one of the the answers. As 3b=4g, i chose a multiple of 4, so 12 would feet... Backsolve and you get the answer... I think by doing setp-by-step ratio will take at least 1.30 min

aj5105 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 the number of boys in Class B is one less than the number of boys in Class A, and if the number of girls in Class B is two less than the number of girls in Class A, how many girls are in Class A?

8
9
10
11
12

I got answer without using the ratio 17:22.

4y = 3x -1
5y = 4x -2

solve and answer. please validate my method.

Your method was awesome.. We really dont need the 17: 22 ratio. We have 2 ratios and we have 2 more conditions given to solve this. It is more than sufficient.

I used the 17/22 ratio and was wondering as to why they gave 2 relations between number of boys and girls of the two classes. I guess your method answers my question.

Class A--(3k1,4k1) and Class B--(4k2,5k2)

eqn is

(3k1+4k2)/(4k2+5k2) = 17/22--------------(A)

given is 4k2+1=3k1; 5k2+2=4k1

now replace 4k2 and 5k2 into main Eqn (A)

and find 4k1=12(hence E)

is this a GMAT type Q?