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?

The question is asking us to find Hank's age given that the ratio of Sam's age to Hank's age is 5 to 3 and that their combined ages add up to 24.
First, we set up the ratio as two algebraic expressions:
5x for Sam's age and 3x for Hank's age, where x is a common multiplier for their ages.
The sum of their ages is:
5x + 3x = 24
This simplifies to
8x = 24.
Solving for x gives us x = 24 ÷ 8, which simplifies to
x = 3.
Therefore, Sam is 5 × 3 = 15 years old, and Hank is 3 × 3 = 9 years old.

Answered by IanMckellen | 2024-06-24

Hank is 9 years old, calculated using the ratio of their ages which is 5 to 3 and the total of their ages being 24. This was done by setting up equations based on the ratio and solving for the ages. Sam is therefore 15 years old.
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Answered by IanMckellen | 2025-02-01