1. **State the problem:** Find another combination of nickels ($x$) and dimes ($y$) that totals 11 coins and equals 0.80 in value. 2. **Recall the equations:** - Total coins: $x + y = 11$ - Total value: $0.05x + 0.10y = 0.80$ 3. **Rewrite the total coins equation:** $y = 11 - x$ 4. **Substitute into the value equation:** $0.05x + 0.10(11 - x) = 0.80$ 5. **Distribute:** $0.05x + 1.10 - 0.10x = 0.80$ 6. **Combine like terms:** $\cancel{0.05x} - 0.10x = -0.05x$ $-0.05x + 1.10 = 0.80$ 7. **Subtract 1.10 from both sides:** $-0.05x = 0.80 - 1.10$ $-0.05x = -0.30$ 8. **Divide both sides by $-0.05$:** $x = \frac{-0.30}{-0.05} = 6$ 9. **Check for other integer solutions:** Since the value equation simplifies to $-0.05x = -0.30$, $x$ must be 6 to satisfy the value exactly. 10. **Try different total coins:** If total coins remain 11, no other integer solution exists for $x$ and $y$ to satisfy the value equation. 11. **Try different total coins:** If total coins change, for example $x + y = 10$, then: $0.05x + 0.10y = 0.80$ Substitute $y = 10 - x$: $0.05x + 0.10(10 - x) = 0.80$ $0.05x + 1.00 - 0.10x = 0.80$ $-0.05x + 1.00 = 0.80$ $-0.05x = -0.20$ $x = 4$ $y = 10 - 4 = 6$ 12. **Answer:** Another possible combination is 4 nickels and 6 dimes totaling 10 coins and 0.80 in value. **Note:** For the original total of 11 coins, only 6 nickels and 5 dimes work to make 0.80.