Math CentralQuandaries & Queries


Question from Jules, a student:

Hi, I am a grade 12 learner, I was helping my brother on ratio in the grade 9 Textbook I found a question that I did not manage to solve, may you please help me to solve it, Thank you.

1a) If 2/3 of the boys and 3/4 of the girls at a party are dancing, what is the ratio of boys to girls, if all the dancing couples consist of a boy and girl?

b) If the total number of the boys and girls of the party is 153, how many boys are at the party?

Hi Jules,

Suppose that there are B boys at the party and G girls, thus when you get to part b) you know that

B + G = 153.

For part a) you know that the number of boys dancing is 2/3 B and the number of girls dancing is 3/4 G. But the number of boys dancing is equal to the number of girls dancing so

2/3 B = 3/4 G


8 B = 9 G.

Thus B/G = 9/8 of said as a ratio

B:G = 9:8.

I hope this helps,

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