Question

Over winter break, Raymond worked 12.5 hours at the library and 20.5 hours at a café. The library paid him $13 per hour. If he earned a total of $459.75 from both jobs, how much did the café pay Raymond per hour?

Answer 1

To find out how much the café paid Raymond per hour, we will first calculate how much he earned from the library and then determine how much he earned from the café.

1. **Calculate earnings from the library:**
Raymond worked 12.5 hours at the library and earned $13 per hour.
\[
\text{Earnings from library} = \text{Hours worked} \times \text{Hourly rate} = 12.5 \text{ hours} \times 13 \text{ dollars/hour} = 162.5 \text{ dollars}
\]

2. **Calculate earnings from the café:**
Let \( x \) be the hourly wage Raymond earned at the café. He worked 20.5 hours at the café, so his earnings from the café can be represented as:
\[
\text{Earnings from café} = 20.5 \text{ hours} \times x \text{ dollars/hour}
\]

3. **Set up the equation based on total earnings:**
The total amount he earned from both jobs is $459.75. Therefore, we can write:
\[
\text{Earnings from library} + \text{Earnings from café} = 459.75
\]
Substituting the earnings from the library:
\[
162.5 + 20.5x = 459.75
\]

4. **Solve for \( x \):**
First, subtract 162.5 from both sides:
\[
20.5x = 459.75 - 162.5
\]
\[
20.5x = 297.25
\]

Next, divide both sides by 20.5 to find \( x \):
\[
x = \frac{297.25}{20.5}
\]
Calculating the right-hand side:
\[
x \approx 14.5
\]

So, the café paid Raymond approximately **$14.50 per hour**.