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Planet Fitness charges a one-time application fee of $50 plus $30 per session for a
personal trainer. Gold's Gym charges an annual fee of $250 plus $10 for each sessio
with a trainer. Write an equation to determine for how many sessions is the cost of the
two plans the same? Explain your expressions.

Respuesta :

calculista

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

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