1. **State the problem:** Kelly and Sarah need at least 12 dollars in change using quarters and dimes. They also need at least six more quarters than dimes. 2. **Define variables:** Let $x$ = number of quarters, $y$ = number of dimes. 3. **Write inequalities for the money amount:** Each quarter is 25 cents, each dime is 10 cents. Total amount in cents is $25x + 10y$. They need at least 12 dollars = 1200 cents. So, $$25x + 10y \geq 1200$$ 4. **Simplify the money inequality:** Divide both sides by 5: $$\frac{\cancel{5}(5x + 2y)}{\cancel{5}} \geq \frac{1200}{5}$$ which simplifies to $$5x + 2y \geq 240$$ 5. **Express $y$ in terms of $x$ from the money inequality:** $$2y \geq 240 - 5x$$ $$y \geq \frac{240 - 5x}{2} = 120 - 2.5x$$ 6. **Write inequality for quarters and dimes difference:** They need at least six more quarters than dimes: $$x \geq y + 6$$ Rearranged: $$y \leq x - 6$$ 7. **Final system of inequalities:** $$y \geq 120 - 2.5x$$ $$y \leq x - 6$$ 8. **Choose the correct option:** The system matches: $$y \geq -2.5x + 120$$ and $$y \leq x - 6$$ **Answer:** $y \geq -2.5x + 120$, $y \leq x - 6$