7
algebra

Tom is 4 years older than his brother. In 3 years, their combined ages will be 30. How old is Tom now?

A

12 years old

B

13 years old

C

14 years old

D

15 years old

Correct Answer: C

Choice C is the correct answer. Let TT = Tom's age now and BB = brother's age now.

System: {T=B+4(T+3)+(B+3)=30\begin{cases} T = B + 4 \\ (T + 3) + (B + 3) = 30 \end{cases}

Step 1: Simplify second: T+B+6=30T + B + 6 = 30T+B=24T + B = 24

Step 2: Substitute: (B+4)+B=24(B + 4) + B = 242B=202B = 20B=10B = 10

Step 3: Find T: T=10+4=14T = 10 + 4 = 14

Solution: Tom is 14 years old

Verification: In 3 years: (14+3)+(10+3)=17+13=30(14+3) + (10+3) = 17 + 13 = 30

💡 Strategic Tip: Age difference is constant over time.

**Other choices fail verification.