Exercise 15 Page 207

Write equations that represent what André and Paul charge.

4 hours

Practice makes perfect

Let's write equations for the amount André and Paul charge. We will use x to represent the number of hours the job takes and y represent the money earned.

Information	Equation
André charges a $30 service fee and $10 per hour.	y=30 + 10 * x
Paul charges a $10 service fee and $15 per hour.	y=10 + 15 * x

To find the time when André and Paul charge the same amount, let's graph these equations. The graph of both of these equations is a line. We can draw these lines through two points, so let's find two points on both lines.

Name	Service Fee		After 1 hour
Name	Expression	Point	Expression	Point
André	30	(0,30)	30+10=40	(1,40)
Paul	10	(0,10)	10+15=25	(1,25)

We then plot these points and draw lines to connect them.

The first coordinate of the point of intersection of these lines gives the time when André and Paul charge the same amount.

We can see from the graph that André and Paul both charge $70 for 4 hours of work.

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