How many different amounts of money can you pay if you use four coins including dimes and quarters? A. 5 amounts B. 4 amounts C. 6 amounts D. 3 amounts

To determine how many different amounts of money can be paid using four coins that include dimes (10 cents) and quarters (25 cents), we can analyze the combinations of these coins. Let's denote: - \( d \) = number of dimes - \( q \) = number of quarters The total number of coins used is given by the equation: \[ d + q = 4 \] Now, we can find the different combinations of dimes and quarters that satisfy this equation: 1. **0 dimes and 4 quarters**: - Amount = \( 0 \times 10 + 4 \times 25 = 100 \) cents 2. **1 dime and 3 quarters**: - Amount = \( 1 \times 10 + 3 \times 25 = 10 + 75 = 85 \) cents 3. **2 dimes and 2 quarters**: - Amount = \( 2 \times 10 + 2 \times 25 = 20 + 50 = 70 \) cents 4. **3 dimes and 1 quarter**: - Amount = \( 3 \times 10 + 1 \times 25 = 30 + 25 = 55 \) cents 5. **4 dimes and 0 quarters**: - Amount = \( 4 \times 10 + 0 \times 25 = 40 \) cents Now, let's summarize the amounts we calculated: - 100 cents - 85 cents - 70 cents - 55 cents - 40 cents These amounts are all different. Therefore, the total number of different amounts of money that can be paid using four coins (including dimes and quarters) is 5. Thus, the answer is: **A. 5 amounts**.