Question

Western State college is 18 years older than southern state. Western is also 2 1\2 times as old as southern. How old is each

Answer 1

let's firstly, convert the mixed fraction to improper, and then check what's cooking.

`\bf \stackrel{mixed}{2(1)/(2)}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} w=\textit{Western State College}\\ s=\textit{Southern State College} \end{cases}~\hspace{5em} \begin{array}{llll} \stackrel{\textit{\underline{w} is 18 more than \underline{s}}}{\boxed{w}=s+18}\\\\ \stackrel{\textit{\underline{w} is }(5)/(2)\textit{ of \underline{s}}}{w=\cfrac{5}{2}s} \end{array}`

`\bf ~\dotfill\\\\ \boxed{s+18}=\cfrac{5}{2}s\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2s+36=5s}\implies 36=3s \\\\\\ \cfrac{36}{3}=s\implies \blacktriangleright 12=s \blacktriangleleft ~\hfill \blacktriangleright \stackrel{w=s+18}{30} \blacktriangleleft`

if you wonder why we multiplied by the LCD of 2, is just to do away with the denominators.