Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
(A) 3
(B) 7
(C) 15
(D) 21
(E) 25
Kudos for a correct solution.
KAPLAN OFFICIAL SOLUTION:The first step to answering this question is translating the information in the problem into equations. If Jacob is 12 years younger than Michael, we can say that J = M – 12, where J is Jacob’s age and M is Michael’s age.
The second equation is a bit trickier to determine. You must keep in mind that it refers to the relationship between their ages in 9 years. Thus, Jacob will be J + 9 years old and Michael will be M + 9 years old. The equation we can then write if Michael will be twice as old as Jacob in 9 years is M + 9 = 2(J + 9).
Because the question wants us to solve for Jacob’s age in 4 years, we should next rewrite our first equation as M = J + 12. This allows us to substitute J + 12 for M in the second equation, which becomes (J + 12) + 9 = 2(J + 9). Then solve for J as follows:
J + 12 + 9 = 2(J + 9)
J + 21 = 2J + 18
3 = J.
However, you must remember that the question asks for Jacob’s age in 4 years. Since Jacob is 3 years old today, we know that he will be 7 years old in 4 years. Thus, the correct answer is
choice (B).
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