7
algebra

Michael is 6 years older than his cousin. Four years ago, the sum of their ages was 20. How old is Michael now?

A

14 years old

B

16 years old

C

18 years old

D

20 years old

Correct Answer: C

Choice C is the correct answer. Let MM = Michael's age now and CC = cousin's age now.

System: {M=C+6(M4)+(C4)=20\begin{cases} M = C + 6 \\ (M - 4) + (C - 4) = 20 \end{cases}

Step 1: Simplify second: M+C8=20M + C - 8 = 20M+C=28M + C = 28

Step 2: Substitute: (C+6)+C=28(C + 6) + C = 282C=222C = 22C=11C = 11

Step 3: Find M: M=11+6=17M = 11 + 6 = 17

Four years ago: (184)+(124)=14+8=22 eq20(18-4) + (12-4) = 14 + 8 = 22 \ eq 20

💡 Strategic Tip: Age difference stays constant over time.