ExplanationAssign variables and translate equations from the given information:

r = Rey’s age NOW

s = Sebastian’s age NOW

\(r = s - 12\)

\((r - 5) = \frac{1}{2}(s - 5)\)

Multiply the second equation by 2 to eliminate the fraction and simplify:

\(2r - 10 = s - 5\)

\(2r = s + 5\)

Since the question asks for Sebastian’s age next year and r is already isolated in the first equation, substitute for r in the adjusted second equation and solve:

\(2(s - 12) = s + 5\)

\(2s - 24 = s + 5\)

\(2s = s + 29\)

\(s = 29\)

If Sebastian is 29 now, he will be 30 next year.

Check the answer. If Sebastian is 29 now, Rey is 17 now. Five years ago, they were 24 and 12, respectively, and 12 is half of 24.

Hence option D is correct!
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Sandy

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