Boys and Girls

Algebra Level 3

Fill in the blank:

In a classroom full of boys and girls,

if 3 boys leave, there will be 4 times as many boys left as girls;
if 3 girls leave, there will be 9 times as many boys left as girls;
if 3 boys and 3 girls leave, there will be _______ \text{\_\_\_\_\_\_\_} times as many boys left as girls.

5 6 7 8

Christopher Boo by Christopher Boo , 24, Singapore

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1 solution

Marta Reece
Jun 15, 2017

Let B = B= number of boys, G = G= number of girls.

Calculating the number of boys from the first equation: B − 3 = 4 G ⟹ B = 4 G + 3 B-3=4G\implies B=4G+3

The same number from the second equation should be equal to it: B = 9 ( G − 3 ) = 4 G + 3 B=9(G-3)=4G+3

Solving for G = 30 5 = 6 G=\dfrac{30}{5}=6

From that the number of boys is: B = 4 G + 3 = 4 × 6 + 3 = 27 B=4G+3=4\times6+3=27

The relationship we need to complete is B − 3 = x ( G − 3 ) B-3=x(G-3)

And it is true for x = 24 3 = 8 x=\dfrac{24}{3}=\boxed{8}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I was surprised that the ratio was integral.

Calvin Lin Staff - 3 years, 11 months ago

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I kinda of expected it, after all, the problem writer can decide what numbers to pick for the subtraction. If it wasn't integral it's likely they would have written "the ratio between B and G" or "the ratio between B+3 and G+3", so it would still look pretty.

Alex Li - 3 years, 11 months ago

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