1997 PMWC Problems/Problem I7

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Problem

40% of girls and 50% of boys in a class got an 'A'. If there are only 12 students in the class who got 'A's and the ratio of boys and girls in the class is 4:5, how many students are there in the class?

Solution

$\frac{2}{5}g + \frac{1}{2}b = 12$ $5b = 4g \Longrightarrow b = \frac{4}{5}g$

Substituting, $\frac{2}{5}g + \frac{1}{2}\left(\frac 45g\right) = 12 \Longrightarrow \frac{4}{5}g = 12 \Longrightarrow g = 15$ . So there are 12 boys, and $12 + 15 = 27$ students in the class.

1997 PMWC (Problems)
Preceded by Problem I6	Followed by Problem I8
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

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1997 PMWC Problems/Problem I7

From AoPSWiki

Problem

Solution

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