Question

The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank?

Answer 1

`S-Sam's\ age\\H-Hank's\ age\\\\ \left\{\begin{array}{ccc}(S)/(H)=(5)/(3)\\S+H=24&\to S=24-H\end{array}\right\\\\substitute\ S=24-H\ to\ (S)/(H)=(5)/(3)\\\\(24-H)/(H)=(5)/(3)\\\\cross\ multiply\\\\5H=3(24-H)\\5H=72-3H\\5H+3H=72\\8H=72\ \ \ /:8\\H=9\\\\Answer:Hank\ is\ 9\ years\ old.`