Question

1) Clare wants to take group fitness classes at a nearby gym, but needs to start by
selecting a membership plan. With the first membership plan, Clare can pay $70 per month,
plus $3 for each group class she attends. Alternately, she can get the second membership
plan and pay $40 per month plus $6 per class. If Clare 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

Using linear functions, she pays the same for 10 classes, which is represented by the graph at the end of the question.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we consider the flat fee as the intercept and the cost per group class as the slope, hence the functions are given by:

• A(x) = 70 + 3x.

• B(x) = 40 + 6x.

She pays the same when:

A(x) = B(x).

70 + 3x = 40 + 6x

3x = 30

x = 10.

Hence when there are 10 classes.

More can be learned about linear functions at https://brainly.com/question/24808124

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