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.

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

where

m is the slope

b is the y-intercept

Planet Fitness

we have

The slope is equal to

The y-intercept or initial value is equal to

substitute

----> equation A

Gold's Gym

we have

The slope is equal to

The y-intercept or initial value is equal to

substitute

----> equation B

Equate equation A and equation B

solve for x

therefore

When the number of sessions is equal to 10, the total cost is the same in the two plans

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.