1.
Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month.
Super Fit charges a one-time registration fee of $150, and membership is $10 a month.
(a) Write a expression to represent the membership cost of Platinum Gym for x months.
Let x = months
20x + 60 is your expression
(b) Write an expression to represent the membership cost of Super Fit for x months
Let x = months
10x + 150 is your expression
(c) You are solving for both one month and twelve months of membership.
<u>One month:</u> Plug in 1 for x.
20(1) + 60 = 20 + 60 = 80
10(1) + 150 = 10 + 150 = 160
Platinum Gym is cheaper overall for one month by $80
<u>One year:</u> There are twelve months in a year. Plug in 12 for x.
20(12) + 60 = 240 + 60 = 300
10(12) + 150 = 120 + 150 = 270
Super Fit is cheaper than Platinum Gym overall for one year by $30
(d) Set the two expression equal to each other.
20x + 60 = 10x + 150
Isolate the x. Subtract 10x and 60 from both sides
20x (-10x) + 60 (-60) = 10x (-10x) + 150 (-60)
20x - 10x = 150 - 60
Simplify
20x - 10x = 150 - 60
10x = 90
Isolate the x. Divide 10 from both sides
10x/10 = 90/10
x = 9
It takes 9 months for the cost to be the same.
(e) It really depends on how long you want to work out at a gym. If you are working out for less than a year, than Platinum Gym is the better choice. If more than a year, then Super Fit is the better choice.
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