Maggie's farm stand sold total of 165 pounds of apples and peaches. She sold apples for $1.75 per ground and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?

Options

A. `11`
B. `18`
C. `65`
D. `100`

Answer

To solve the problem step by step, we will define variables, set up equations based on the information given, and then solve for the unknowns.

### Step 1: Define Variables
Let:
- \( x \) = the number of pounds of apples sold
- \( y \) = the number of pounds of peaches sold

### Step 2: Set Up the Equations
From the problem, we know:
1. The total weight of apples and peaches sold is 165 pounds:
\[ x + y = 165 \quad \text{(Equation 1)} \]

2. The total earnings from selling apples and peaches is $337.50. The price per pound for apples is $1.75 and for peaches is $2.50:
\[ 1.75x + 2.50y = 337.50 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for \( x \)
From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 165 - y \]

### Step 4: Substitute \( x \) in Equation 2
Now, substitute \( x \) in Equation 2:
\[ 1.75(165 - y) + 2.50y = 337.50 \]

### Step 5: Distribute and Simplify
Distributing \( 1.75 \):
\[ 1.75 \times 165 - 1.75y + 2.50y = 337.50 \]
Calculating \( 1.75 \times 165 \):
\[ 288.75 - 1.75y + 2.50y = 337.50 \]
Combining like terms:
\[ 288.75 + 0.75y = 337.50 \]

### Step 6: Isolate \( y \)
Now, isolate \( y \):
\[ 0.75y = 337.50 - 288.75 \]
Calculating the right side:
\[ 0.75y = 48.75 \]

### Step 7: Solve for \( y \)
Now, divide both sides by 0.75:
\[ y = \frac{48.75}{0.75} = 65 \]

### Step 8: Conclusion
Thus, the number of pounds of peaches sold is:
\[ \boxed{65} \]

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