Set 10: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Let $L$ = Lisa's age now and $S$ = sister's age now. System: $\begin{cases} L = 2 S \\ (L - 5) + (S - 5) = 25 \end{cases}$ Step 1: Simplify second equation: $L + S - 10 = 25L + S = 35$ Step 2: Substitute $L = 2 S$: $$$2S + S = 353S = 35$S = \frac{35}{3} Five years ago: Lisa was 15 and sister was 5. Sum: $15+ 5 = 20 \neq 25$. Sister = 12. Five years ago: $19+ 7 = 26 \neq 25$. $2S + S = 35$, so $S = \frac{35}{3}$ which isn't an integer. $S = 10$ (sister) Five years ago: $(20-5) + (10-5) = 15 + 5 = 20$ Strategic Tip: Age difference remains constant; work backwards from "years ago." Choice A is incorrect because if Lisa is 15, sister is 7.5 (not integer). Choice B is incorrect because if Lisa is 18, sister is 9. Five years ago: $13+ 4 = 17 \neq 20$. Choice D is incorrect because if Lisa is 24, sister is 12. Five years ago: $19+ 7 = 26 \neq 20$.