1. **State the problem:** We have 22 coins total, consisting of dimes and nickels, with a total value of 1.90 dollars. We want to find the system of equations that models this situation using $d$ for dimes and $n$ for nickels. 2. **Define variables:** - $d$ = number of dimes - $n$ = number of nickels 3. **Write the equations:** - Total coins: $d + n = 22$ - Total value: Each dime is worth 0.10 dollars and each nickel is worth 0.05 dollars, so the value equation is $0.10d + 0.05n = 1.90$ 4. **Check the options:** - Option A: $d + n = 1.9$ (incorrect total coins), $0.1d + 0.05n = 22$ (incorrect value) - Option B: $d + n = 22$ (correct total coins), $0.1d + 0.05n = 1.9$ (correct value) - Option C: $d + n = 1.9$ (incorrect total coins), $0.1d + 0.5n = 22$ (incorrect value) - Option D: $d + n = 22$ (correct total coins), $0.1d + 0.5n = 1.9$ (incorrect value coefficient for nickels) 5. **Conclusion:** The correct system is option B. **Final answer:** $$\begin{cases} d + n = 22 \\ 0.1d + 0.05n = 1.9 \end{cases}$$