# SAT/ACT problem of the week, December 29, 2016 solution

Hint for process of elimination: The largest part of the student body population consists of girls. Therefore, the population of girls is greater than $latex \dfrac{1}{3}$, or 33.3%, of the total population. This at least eliminating choice A. But the ratio of girls to girls plus boys is $latex \dfrac{150\%}{150\%+100\%}=3/5$, or 60%. Therefore the population of girls is under 60%. That at least eliminates both D and E. Answer C is too nice for this particular complex situation, and is also meant to draw your eye since the number $Latex 50\%$ appears twice in the problem, so I lean towards B.

Read on for a full solution.

Solution: The sentences in this problem are word equations.

(The number of girls) [is] (50% more than) (the number of chimpanzees).
$latex \text{(The number of girls)} = \text{(the number of chimpanzees)} + \text{(50\% of the number of chimpanzees)}$
$latex g = c +.5c = 1.5c$

(The number of chimpanzees) [is] (50% more than) (the number of boys).
$latex c = b + .5b = 1.5b$

The total student population, as a multiple of girls, is $latex g + c + b = g + c + \dfrac{c}{1.5} = g + \dfrac{g}{1.5} + \dfrac{g}{1.5 \times 1.5} = g \left( 1 + \frac{1}{1.5} + \frac{1}{2.25} \right)$

So the percentage of girls in the school is $latex \dfrac{\not{g}1}{\not{g} \left(1 + \frac{1}{1.5} + \frac{1}{2.25}\right) } \times 100 \%\approx 47\%$

Work it out! Make sure you get the same answer.