When you post a problem, please include the answer choices.
In ten years, Paul will be twice as old as Michael. Fifteen years ago, Paul was five times as old as Vanessa. Vanessa is eight years older than Michael. How old is Michael?
(A) 5
(B) 10
(C) 18
(D) 24
(E) 34
We can plug in the answers, which represent Michael's current age.
When the correct answer choice is plugged in, Paul's age in 10 years will be twice Michael's age in 10 years.
Answer choice D: Michael's age = 24
Since Vanessa is 8 years older than Michael, Vanessa's age = 24+8 = 32.
Thus, Vanessa's age 15 years ago = 32-15 = 7.
Since 15 years ago Paul was 5 times as old as Vanessa, Paul's age 15 years ago = 5*7 = 35.
Since 15 years ago Paul was 35, Paul's current age = 35+15 = 50.
In 10 years, Paul's age = 50+10 = 60.
In 10 years, Michael's age = 24+10 = 34.
Doesn't work: 60/34 ≠2.
Eliminate D.
Answer choice B: Michael's age = 10
Since Vanessa is 8 years older than Michael, Vanessa's age = 10+8 = 18.
Thus, Vanessa's age 15 years ago = 18-15 = 3.
Since 15 years ago Paul was 5 times as old as Vanessa, Paul's age 15 years ago = 5*3 = 15.
Since 15 years ago Paul was 15, Paul's current age = 15+15 = 30.
In 10 years, Paul's age = 30+10 = 40.
In 10 years, Michael's age = 10+10 = 20.
Success!
40/20 = 2.
The correct answer is
B.
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