1. **State the problem:** Jackson has quarters (q) and dimes (d). The total value is 12.65 dollars. The number of quarters is seven less than twice the number of dimes. 2. **Define variables:** Let $q$ = number of quarters, $d$ = number of dimes. 3. **Write equations:** - Value equation: Each quarter is 0.25 dollars, each dime is 0.10 dollars, so total value is $$0.25q + 0.10d = 12.65$$ - Relationship between coins: $$q = 2d - 7$$ 4. **Substitute $q$ from second equation into first:** $$0.25(2d - 7) + 0.10d = 12.65$$ 5. **Simplify:** $$0.5d - 1.75 + 0.10d = 12.65$$ $$0.6d - 1.75 = 12.65$$ 6. **Solve for $d$:** $$0.6d = 12.65 + 1.75 = 14.4$$ $$d = \frac{14.4}{0.6} = 24$$ 7. **Find $q$ using $q = 2d - 7$:** $$q = 2(24) - 7 = 48 - 7 = 41$$ **Final answer:** Jackson has 41 quarters and 24 dimes. **System of equations:** $$\begin{cases} 0.25q + 0.10d = 12.65 \\ q = 2d - 7 \end{cases}$$