Tom is 2 years older than Sue and Bill is twice as old as Tom.If you add all their ages and subtract 2, the sum is 20.How old is Bill?
Question
Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill?
Solution
Let's solve this step by step:
- Let's denote Sue's age as S. According to the problem, Tom is 2 years older than Sue, so Tom's age is S + 2.
- Bill is twice as old as Tom, so Bill's age is 2 * (S + 2) = 2S + 4.
- If you add all their ages and subtract 2, the sum is 20. So, S + (S + 2) + (2S + 4) - 2 = 20.
- Simplifying the equation, we get 4S + 4 = 20.
- Subtract 4 from both sides, we get 4S = 16.
- Divide both sides by 4, we get S = 4. So, Sue is 4 years old.
- Substituting S = 4 into the equation for Bill's age, we get Bill's age = 2 * (4 + 2) = 12.
So, Bill is 12 years old.
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