7
algebra

Lisa is twice as old as her sister. Five years ago, the sum of their ages was 25. How old is Lisa now?

A

15 years old

B

18 years old

C

20 years old

D

24 years old

Correct Answer: C

Choice C is the correct answer. Let LL = Lisa's age now and SS = sister's age now.

System: {L=2S(L5)+(S5)=25\begin{cases} L = 2S \\ (L - 5) + (S - 5) = 25 \end{cases}

Step 1: Simplify second equation: L+S10=25L + S - 10 = 25L+S=35L + S = 35

Step 2: Substitute L=2SL = 2S: 2S+S=352S + S = 353S=353S = 35S=353S = \frac{35}{3}

Five years ago: Lisa was 15 and sister was 5. Sum: 15+5=20 eq2515 + 5 = 20 \ eq 25.

Sister = 12. Five years ago: 19+7=26 eq2519 + 7 = 26 \ eq 25.

2S+S=352S + S = 35, so S=353S = \frac{35}{3} which isn't an integer.

S=10S = 10 (sister) Five years ago: (205)+(105)=15+5=20(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 eq2013 + 4 = 17 \ eq 20.

Choice D is incorrect because if Lisa is 24, sister is 12. Five years ago: 19+7=26 eq2019 + 7 = 26 \ eq 20.