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Ratio problem

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Source: — Problem Solving |

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by [email protected] » Mon Mar 07, 2016 10:27 pm
Hi didieravoaka,

We're told that the ratio of boys to girls is 3:4. Next we're told that there are 5 more girls than boys. We're asked for the number of girls in the club.

Since the ratio is 3 to 4, that means that the number of boys MUST be a multiple of 3 and the number of girls must be an equivalent multiple of 4.

Since the number of girls is only 5 more than the number of boys, we can approach the math in a variety of ways, including 'brute force':

3 boys and 4 girls = 1 more girl
6 boys and 8 girls = 2 more girls
9 boys and 12 girls = 3 more girls
12 boys and 16 girls = 4 more girls
15 boys and 20 girls = 5 more girls

Increasing the number of boys and girls will just increase the difference between them, so we can stop here.

Final Answer: E

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by Matt@VeritasPrep » Thu Mar 17, 2016 9:16 pm
You could always use the answers. We know the number of girls = (a multiple of 3) + 5, so the answer must be 8 or 20. But 8 is too small: if that's our answer, we'd have 3 girls and 4 boys, which doesn't fit the second equation. (We need Girls = Boys + 5.) So the answer must be 20, and we're done!
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