Set 4: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. Let $E$ = Emma's current age and $J$ = Jake's current age. Step 1: Set up the system: $\begin{cases} E = J + 8 \\ (E + 5) + (J + 5) = 36 \end{cases}$ Step 2: Simplify second equation: $E + J + 10 = 36E + J = 26$ Step 3: Substitute $E = J + 8$: (J + 8) + J = 26$2J + 8 = 262J = 18J = 9$$ Step 4: Find E: $$E = 9 + 8 = 17$$ Solution: Emma is 17 years old now (Jake is 9) Verification: Emma is 8 years older ✓. In 5 years: (17+5) + (9+5) = 22 + 14 = 36$ ✓ Strategic Tip: Age problems: age difference stays constant over time. Choice A is incorrect because if Emma is 15, Jake is 7. In 5 years: $20+ 12 = 32 \neq 36$. Choice C is incorrect because if Emma is 18, Jake is 10. In 5 years: $23+ 15 = 38 \neq 36$. Choice D is incorrect because if Emma is 20, Jake is 12. In 5 years: $25+ 17 = 42 \neq 36$.