Question:
A is three years older than B who is twice as old as C. If the sum of the ages of A, B and C is 28 years, then how old is B?
A is three years older than B who is twice as old as C. If the sum of the ages of A, B and C is 28 years, then how old is B?
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Translate word problems into algebraic equations step-by-step using variables for unknowns. Keep track of relationships like "older than" or "twice as old".
Updated On: Apr 21, 2025
- 7 years
- 8 years
- 9 years
- 10 years
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The Correct Option is D
Solution and Explanation
Let C's age be \( x \) years.
Then,
- B = \( 2x \) (since B is twice as old as C)
- A = \( 2x + 3 \) (A is 3 years older than B)
Now, sum of their ages:
\[
A + B + C = (2x + 3) + 2x + x = 5x + 3
\]
Given:
\[
5x + 3 = 28 \Rightarrow 5x = 25 \Rightarrow x = 5
\]
So,
- B = \( 2x = 10 \) years
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