Question

PLEASE URGENT


Mary wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Mary can pay $70 per month, plus $1 for each group class she attends. Alternately, she can get the second membership plan and pay $10 per month plus $4 per class. If Mary attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that?
Write a system of equations, graph them, and type the solution.

Answer 1

The linear equations for the system: y = x + 70 and y = 4x + 10

She'll attend 20 classes/month

The graph for the solution (20, 95) is in the image attached below

What is a Linear Equation?

A linear equation can expressed in slope-intercept form, as, y = mx + b.

• m = unit rate/slope
• b = initial value/y-intercept

Linear equation for the first membership plan:

b = 70

m = 1

x = number of classes

y = total amount

Equation for the first membership plan: y = x + 70

Linear equation for the second membership plan:

b = 10

m = 4

x = number of classes

y = total amount

Equation for the second membership plan: y = 4x + 10

The system of equations are:

y = x + 70

y = 4x + 10

The solution is the point at which the line for both equations intersect on the graph as shown in the image attached below, which is: (20, 95).

This means Mary must attend 20 classes for each membership plan, she must attend 20 classes to pay the same total amount of $95 per month.

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