Question

Boardman's Department Store sells clothing for children and adults. Last weekend the store sold 5 adult shirt's for every 3 children's shirts.
If the store sold 30 more adult shirts than children's shirts last weekend, how many shirts the the store sell?

Answer 1

a = adult shirts sold

c = children shirts sold

we know the store sold for every 5 "a", there were 3 "c" sold, so we can say that the adult to children shirts are on a 5 : 3 ratio.

We also know that whatever "c" is, adult shirts sold last weekend was 30 more than that, or namely "c + 30".

$\stackrel{\textit{\large ratios}}{\cfrac{\stackrel{adult}{a}}{\underset{children}{c}}~~ = ~~\cfrac{5}{3}}\qquad \implies \qquad \stackrel{\textit{we also know that \underline{a = c + 30}}}{\cfrac{c+30}{c}~~ = ~~\cfrac{5}{3}} \\\\\\ 3c+90=5c\implies 90 = 2c\implies \cfrac{90}{2}=c\implies \boxed{45=c}~\hfill \stackrel{c + 30}{\boxed{a=75}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{total~sold}{120}~\hfill$