Michael needs a printing job completed. Photoperfect Print Shop charges a fixed fee of `$3` for the print job and 5 cents per page. Bargain Printing charges a fixed fee of `$2` for the point job and 7 cents per page. P represents the number of pages being printed, what are all values of p for which Photoperfect Print Shop's total charge is less than Bargain Printing's total charge.

Options

A. `plt20`
B. `20leple35`
C. `35leple50`
D. `pgt50`

Answer

To solve the problem, we need to compare the total charges of Photoperfect Print Shop and Bargain Printing based on the number of pages (P) being printed.

### Step-by-step Solution:

1. **Define the Charges**:
- **Photoperfect Print Shop**: Charges a fixed fee of $3 and 5 cents per page.
- **Bargain Printing**: Charges a fixed fee of $2 and 7 cents per page.

2. **Convert Cents to Dollars**:
- Since 1 cent = $0.01, we convert the per-page charges:
- Photoperfect's charge per page: \(5 \text{ cents} = 5 \times 0.01 = 0.05\) dollars.
- Bargain's charge per page: \(7 \text{ cents} = 7 \times 0.01 = 0.07\) dollars.

3. **Write the Total Charge Equations**:
- For Photoperfect Print Shop:
\[ \text{Charge}_{\text{Photoperfect}} = 3 + 0.05P \]
- For Bargain Printing:
\[ \text{Charge}_{\text{Bargain}} = 2 + 0.07P \]

4. **Set Up the Inequality**:
- We want to find when Photoperfect's charge is less than Bargain's charge:
\[ 3 + 0.05P < 2 + 0.07P \]

5. **Simplify the Inequality**:
- Subtract 2 from both sides:
\[ 1 + 0.05P < 0.07P \]
- Subtract \(0.05P\) from both sides:
\[ 1 < 0.02P \]

6. **Solve for P**:
- Divide both sides by 0.02:
\[ P > \frac{1}{0.02} \]
- Calculate \(\frac{1}{0.02}\):
\[ P > 50 \]

### Conclusion:
The values of \(P\) for which Photoperfect Print Shop's total charge is less than Bargain Printing's total charge are:
\[ P > 50 \]