# Difference between revisions of "1997 PMWC Problems/Problem I7"

## Problem

$40\%$ of girls and $50\%$ of boys in a class got an $\mathrm{'A'}$. If there are only $12$ students in the class who got $\mathrm{'A'}$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.