Question

At a local fitness​ center, members pay a ​$10 membership fee and ​$4 for each aerobics class. Nonmembers pay ​$5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the​ same?

(Type in a whole number)

Answer 1

Solve the system by graphing. Tell whether the system has one​ solution, infinitely many​ solutions, or no solution.

y - x = 5

4y = 4x + 20

Answer 2

Let's say the number of aerobics classes is x.

For members, the cost is the membership fee plus $4 for each class:
Cost for members = $10 + $4x

For nonmembers, the cost is $5 for each class:
Cost for nonmembers = $5x

We need to find the value of x for which the cost for members and nonmembers is the same:
$10 + $4x = $5x

Rearranging the equation:
$4x - $5x = -$10
-$x = -$10
x = 10

Therefore, for 10 aerobics classes, the cost for members and nonmembers will be the same.

Answer 3

Let's rearrange each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

First equation:
y - x = 5
Rearranging, we get: y = x + 5

Second equation:
4y = 4x + 20
Dividing both sides by 4, we get: y = x + 5

Comparing both equations, we can see that they are the same equation. The system is graphed as a single line.

This means that the system has infinitely many solutions since any point on the line satisfies both equations.