Answer:
When the number of sessions is equal to 10, the total cost is the same in the two plans
Step-by-step explanation:
Let
y ---> the total cost
x ---> the number of sessions
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
Planet Fitness
we have
The slope is equal to
[tex]m=\$30\ per\ session[/tex]
The y-intercept or initial value is equal to
[tex]b=\$50[/tex]
substitute
[tex]y=30x+50[/tex] ----> equation A
Gold's Gym
we have
The slope is equal to
[tex]m=\$10\ per\ session[/tex]
The y-intercept or initial value is equal to
[tex]b=\$250[/tex]
substitute
[tex]y=10x+250[/tex] ----> equation B
Equate equation A and equation B
[tex]30x+50=10x+250[/tex]
solve for x
[tex]30x-10x=250-50\\20x=200\\x=10[/tex]
therefore
When the number of sessions is equal to 10, the total cost is the same in the two plans
