Set 7: Systems of Equations

Choice C is correct. Choice C is the correct answer. Let $T$ = Tom's age now and $B$ = brother's age now. System: $\begin{cases} T = B + 4 \\ (T + 3) + (B + 3) = 30 \end{cases}$ Step 1: Simplify second: $T + B + 6 = 30T + B = 24$ Step 2: Substitute: (B + 4) + B = 24$2B = 20$B = 10 Step 3: Find T: $T = 10 + 4 = 14$ Solution: Tom is 14 years old Verification: In 3 years: $(14+3) + (10+3) = 17 + 13 = 30$ ✓ Strategic Tip: Age difference is constant over time. Other choices fail verification.