To determine the hourly rate of pay for Piper and Jai, we need to examine the information provided.
### Step 1: Calculate Piper's Hourly Rate of Pay
We have Piper's earnings and hours worked:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Hours } (x) & \text{Earnings } (y) \\
\hline 2 & \$39 \\
\hline 6 & \$117 \\
\hline 10 & \$195 \\
\hline 14 & \$273 \\
\hline
\end{array}
\][/tex]
To find Piper's hourly rate, we look at the change in earnings over the change in hours.
Using the earnings at the two endpoints:
[tex]\[
\Delta y = 273 - 39 = 234 \text{ dollars}
\][/tex]
[tex]\[
\Delta x = 14 - 2 = 12 \text{ hours}
\][/tex]
So, Piper’s hourly rate is:
[tex]\[
\text{Hourly rate} = \frac{\Delta y}{\Delta x} = \frac{234 \text{ dollars}}{12 \text{ hours}} = 19.5 \text{ dollars/hour}
\][/tex]
### Step 2: Calculate Jai's Hourly Rate of Pay
Jai worked for 15 hours and earned [tex]$229.50. Hence, Jai's hourly rate is:
\[
\text{Hourly rate} = \frac{\$[/tex]229.50}{15 \text{ hours}} = 15.3 \text{ dollars/hour}
\]
### Summary
- Piper’s hourly rate is 19.5 dollars per hour.
- Jai’s hourly rate is 15.3 dollars per hour.
Using these values, you can form true statements:
- Piper earns more per hour compared to Jai.
- Jai's hourly rate is 15.3 dollars per hour.
- Piper's hourly rate is 19.5 dollars per hour.
