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?

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17-04-2014
Mathematics

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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?

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Анонимidn Анонимidn · Answer 1 · 2014-04-20T11:08:41-04:00

Анонимidn Анонимidn

20-04-2014

[tex]S-Sam's\ age\\H-Hank's\ age\\\\ \left\{\begin{array}{ccc}\frac{S}{H}=\frac{5}{3}\\S+H=24&\to S=24-H\end{array}\right\\\\substitute\ S=24-H\ to\ \frac{S}{H}=\frac{5}{3}\\\\\frac{24-H}{H}=\frac{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.[/tex]

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