Question

The sum of the two numbers is 80. the ratio two numbers is 3:5 fund the larger number.

PLEASE HELP

Answer 1

`\bf \textit{The sum of the two numbers is 80}\implies a+b=80 \\\\\\ \textit{the ratio of the two numbers is 3:5}\implies \cfrac{a}{b}=\cfrac{3}{5}\\\\ -------------------------------\\\\ a+b=80\implies \boxed{a=80-b} \\\\\\ \cfrac{a}{b}=\cfrac{3}{5}\implies \cfrac{\boxed{80-b}}{b}=\cfrac{3}{5}\implies 5(80-b)=3b\implies 400-5b=3b \\\\\\ 400=8b\implies \cfrac{400}{8}=b\implies 50=b`

the larger ratio is the "5" one, thus that is the larger number.