Exercise 21 Page 367

To find the solution to the problem, we will write two equations and solve the system they form.

Writing the System

One equation in the system will represent the total cost for members. We are told that each person pays a one-time-fee of $20, plus $3 for each aerobic class. Letting x be the number of classes and y be the total amount paid, we get our first equation. y= 3x + 20 Next, we know that non-members do not pay the initial fee, but they pay $5 for each class. Using the same variables as above, we can form our second equation. y= 5x The two equations we have just written form a system of linear equations. y=3x+20 & (I) y=5x & (II)

Solving the System

To find the solution to the system, we will graph both lines in the same coordinate plane and look at the coordinates of the point of intersection, if any. Let's start by drawing the first equation, which is written in slope-intercept form. y= 3x + 20 We will plot the y-intercept 20 and use the slope 3 to find another point on the line. Then, we will connect those points using a straightedge.

Let's consider our second equation next. y= 5x The slope and y-intercept of this equation are 5 and 0, respectively. We will draw its graph following the same procedure as before and consider the point of intersection.

We see the lines intersect at ( 10, 50). In the context of the exercise, this means that members and nonmembers will have paid an equal amount, $50, after 10 classes.