Question

Xavier works 20 hours each week at his part-time job. His manager has promised him a 15% pay raise starting next month. Once he receives his raise, Xavier will make $253 a week.
Which equation can you use to find Xavier's current hourly pay rate, x?
What is Xavier's current hourly pay rate?
$
per hour

Answer 1

To find Xavier's current hourly pay rate, we can start by establishing the relationship between his current pay and how the pay raise will affect it.

1. **Current Pay Calculation**: Let \( x \) be Xavier's current hourly pay rate.
2. **Weekly Pay Calculation**: Since he works 20 hours a week, his current weekly pay can be expressed as:
\[
\text{Current weekly pay} = 20x
\]

3. **New Pay Rate Calculation**: After the 15% raise, his pay will be:
\[
\text{New weekly pay} = 20x + 0.15(20x) = 20x(1 + 0.15) = 20x(1.15)
\]
This expression represents his new weekly pay after the raise.

4. **Setting Up the Equation**: We know that after the raise, his weekly pay will be $253. Therefore, we can set up the equation:
\[
20x(1.15) = 253
\]

5. **Solving for \( x \)**:
\[
20x \cdot 1.15 = 253
\]
Dividing both sides by 1.15:
\[
20x = \frac{253}{1.15}
\]

Calculating the division:
\[
20x \approx 220
\]

Now, divide both sides by 20 to find \( x \):
\[
x = \frac{220}{20} = 11
\]

Thus, Xavier's current hourly pay rate is \(\$11\) per hour.

### Summary:
- **Equation**: \( 20x(1.15) = 253 \)
- **Current hourly pay rate**: \(\$11\) per hour.