Question

A fitness club has two options, one for members and one for nonmembers. Members pay a one-time registration fee of $12 plus $8 per gym visit. Nonmembers pay $10 per gym visit.
Upload a graph

Type the system of equations you used to graph the solutions. Use C for the cost of the two payment options and n for number of visits.

After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option? Explain how you determined your answer.

Answer 1

Answer:

Part 1) The system of equations is

$C=8n+12$ ----> equation 1

$C=10n$ ----> equation 2

Part 2) The graph in the attached figure

Part 3) The number of gym visits must be greater than 6

Step-by-step explanation:

step 1

Find the system of equations that represent the situation

Let

C ----> the total cost in dollars

n ---> the number of gym visits

we know that

The linear equation in slope intercept form is equal to

$C=m(n)+b$

where

m is the slope or unit rate of the linear equation

b is the C-intercept or initial value of the linear equation

First payment option ---> For Members

we have that

The slope or unit rate is equal to $m=\ 8\ per\ gym\ visit$

The C-intercept or initial value is $b=\ 12$ --->one-time registration fee

substitute

$C=8n+12$

Second payment option ---> For Non-Members

we have that

The slope or unit rate is equal to $m=\ 10\ per\ gym\ visit$

The C-intercept or initial value is $b=\ 0$

substitute

$C=10n$

we have

$C=8n+12$ ----> equation 1

$C=10n$ ----> equation 2

Part 2) Upload a graph

using a graphing tool

The graph in the attached figure  

Part 3) After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option?

we know that

If the payment for the member option is more beneficial than the payment for the nonmember option, then the cost for the member option is less than the cost for the nonmember option

so

The inequality that represent this situation is

$8n+12 < 10n$

solve for n

subtract 8n both sides

$12 < 10n-8n$

$12 < 2n$

Divide by 2 both sides

$6 < n$

Rewrite

$n > 6$

therefore

The number of gym visits must be greater than 6