Answer:
Part 1) The system of equations is
[tex]C=8n+12[/tex] ----> equation 1
[tex]C=10n[/tex] ----> 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
[tex]C=m(n)+b[/tex]
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 [tex]m=\$8\ per\ gym\ visit[/tex]
The C-intercept or initial value is [tex]b=\$12[/tex] --->one-time registration fee
substitute
[tex]C=8n+12[/tex]
Second payment option ---> For Non-Members
we have that
The slope or unit rate is equal to [tex]m=\$10\ per\ gym\ visit[/tex]
The C-intercept or initial value is [tex]b=\$0[/tex]
substitute
[tex]C=10n[/tex]
we have
[tex]C=8n+12[/tex] ----> equation 1
[tex]C=10n[/tex] ----> 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
[tex]8n+12 < 10n[/tex]
solve for n
subtract 8n both sides
[tex]12 < 10n-8n[/tex]
[tex]12 < 2n[/tex]
Divide by 2 both sides
[tex]6 < n[/tex]
Rewrite
[tex]n > 6[/tex]
therefore
The number of gym visits must be greater than 6
