Laura has 20 coins consisting of quarters and dimes. If she has a total of $3.05, how many dimes does she have?

Options

A. 3
B. 7
C. 10
D. 13

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let:
- \( Q \) = number of quarters
- \( D \) = number of dimes

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of coins is 20:
\[ Q + D = 20 \quad \text{(Equation 1)} \]

2. The total value of the coins is $3.05, which can be expressed in cents as 305 cents. The value of the coins can be expressed as:
\[ 25Q + 10D = 305 \quad \text{(Equation 2)} \]

### Step 3: Solve for One Variable
From Equation 1, we can express \( Q \) in terms of \( D \):
\[ Q = 20 - D \]

### Step 4: Substitute into the Second Equation
Now, substitute \( Q \) into Equation 2:
\[ 25(20 - D) + 10D = 305 \]

### Step 5: Simplify the Equation
Distributing the 25:
\[ 500 - 25D + 10D = 305 \]
Combine like terms:
\[ 500 - 15D = 305 \]

### Step 6: Solve for \( D \)
Now, isolate \( D \):
\[ -15D = 305 - 500 \]
\[ -15D = -195 \]
\[ D = \frac{-195}{-15} = 13 \]

### Step 7: Find the Number of Quarters
Now that we have \( D \), we can find \( Q \):
\[ Q = 20 - D = 20 - 13 = 7 \]

### Conclusion
Laura has **13 dimes**.

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