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Casey wants to a gym membership one gym has $100 joining fee and costs $30 per month. Another gym has no joining fee and costs $50 per month. When would Casey pay the same to be a member of either gym? How much would he pay?

Respuesta :

calculista

Answer:

Casey would pay the same to be a member of either gym for a number of months equal to 5 and he would pay $250

Step-by-step explanation:

Let

x ----> the number of months

y ----> the total cost in dollars

we know that

The linear equation in slope intercept form between two variables x and y is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

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

In this problem we have

First Gym

The slope or unit rate is equal to [tex]m=\$30\ per\ month[/tex]

The y-intercept or initial value is [tex]b=\$100[/tex] ----> joining fee

so

[tex]y=30x+100[/tex] ----> equation A

Second Gym

The slope or unit rate is equal to [tex]m=\$50\ per\ month[/tex]

The y-intercept or initial value is [tex]b=\$0[/tex] ----> joining fee

so

[tex]y=50x[/tex] ----> equation B (proportional relationship)

equate equation A and equation B

[tex]50x=30x+100[/tex]

solve for x

[tex]50x-30x=100[/tex]

[tex]20x=100[/tex]

[tex]x=5\ months[/tex]

Verify

For x=5

First Gym

[tex]y=30(5)+100=\$250[/tex]

Second Gym

[tex]y=50(5)=\$250[/tex]

therefore

Casey would pay the same to be a member of either gym for a number of months equal to 5 and he would pay $250

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