Question

two friends, skylar and aaron, took summer jobs. aaron earned $520.80 in 24 hours. the graph below represents skylars earnings in dollars and cents, y, for working x hours. skylars earnings (20,$564) (10,$282) how much less per hour does aaron earn than skylar?

Explanation:

Step1: Find Skylar's hourly rate

To find Skylar's hourly rate, we can use the two points on the graph \((10, 282)\) and \((20, 564)\). The slope of the line (which represents the hourly rate) is calculated by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{564 - 282}{20 - 10}=\frac{282}{10} = 28.2\) dollars per hour.
We can also check with the origin \((0,0)\) and \((10,282)\): \(m=\frac{282-0}{10 - 0}=28.2\) dollars per hour.

Step2: Find Aaron's hourly rate

Aaron earned \(\$520.80\) in \(24\) hours. The hourly rate is calculated by dividing the total earnings by the number of hours. So, Aaron's hourly rate \(=\frac{520.80}{24}=21.7\) dollars per hour.

Step3: Find the difference

To find how much less Aaron earns per hour than Skylar, we subtract Aaron's hourly rate from Skylar's hourly rate.
Difference \(=28.2-21.7 = 6.5\) dollars per hour.

Answer:

\(6.5\) dollars