A store sells shirts fro $7.50 each and hats for $5.00 each. The store earns $1,822.50 in one day from selling a total of 307 shirts and hats. How many shirts were sold on that day?

Options

A. `37`
B. `89`
C. `115`
D. `202`

Answer

To solve the problem, we will set up a system of equations based on the information given.

### Step 1: Define the Variables
Let:
- \( X \) = number of shirts sold
- \( Y \) = number of hats sold

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of shirts and hats sold is 307:
\[ X + Y = 307 \quad \text{(Equation 1)} \]

2. The total earnings from selling shirts and hats is $1,822.50:
\[ 7.50X + 5.00Y = 1822.50 \quad \text{(Equation 2)} \]

### Step 3: Solve for One Variable
We can solve Equation 1 for \( Y \):
\[ Y = 307 - X \]

### Step 4: Substitute into the Second Equation
Now, substitute \( Y \) in Equation 2:
\[ 7.50X + 5.00(307 - X) = 1822.50 \]

### Step 5: Simplify the Equation
Distributing the 5.00:
\[ 7.50X + 1535 - 5.00X = 1822.50 \]

Combine like terms:
\[ (7.50 - 5.00)X + 1535 = 1822.50 \]
\[ 2.50X + 1535 = 1822.50 \]

### Step 6: Isolate \( X \)
Subtract 1535 from both sides:
\[ 2.50X = 1822.50 - 1535 \]
\[ 2.50X = 287.50 \]

### Step 7: Solve for \( X \)
Divide both sides by 2.50:
\[ X = \frac{287.50}{2.50} \]
\[ X = 115 \]

### Conclusion
The number of shirts sold on that day is \( \boxed{115} \).

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