The equation that shows the membership cost for Platinum gym is
y = 30x + 90
The equation that shows the membership cost for Super Fit is
y = 20x + 200
Tom would pay $270 to join Platinum gym for 6 months
Tom would pay $320 to join Super Fit for 6 months
It costs the same amount of money for both gyms after 11 month
For the number of months lass than 11 month Platinum gym is the
better deal
For the number of months greater than 11 month Super Fit is the
better deal
Step-by-step explanation:
Tom saw that Platinum gym has a sale with a one time fee of $90 and
a monthly fee of $30
Tom's friend sees that Super Fit only charges $20 a month, but its
registration fee is $200
To write an equation that shows the membership cost for each gym
do that:
1. Assume that the number of months for the membership is x
2. Assume that the cost for the membership in x month is y
3. Write the linear equation y = mx + c, where m is the monthly fee and
c is the registration fee (one-time fee)
Platinum gym:
∵ The monthly fee is $30
∵ One time fee is $90
∵ The number of months is x
∴ The cost of the membership is ⇒ y = 30x + 90
The equation that shows the membership cost for Platinum gym is
y = 30x + 90
Super Fit:
∵ The monthly fee is $20
∵ One time fee is $200
∵ The number of months is x
∴ The cost of the membership is ⇒ y = 20x + 200
The equation that shows the membership cost for Super Fit is
y = 20x + 200
∵ Tom joins Platinum gym for 6 months
∴ x = 6
∵ y = 30x + 90
To find the cost of the 6 months substitute x by 6 in the equation
∴ y = 30(6) + 90
∴ y = 180 + 90
∴ y = 270
Tom would pay $270 to join Platinum gym for 6 months
∵ Tom joins Super Fit for 6 months
∴ x = 6
∵ y = 20x + 200
To find the cost of the 6 months substitute x by 6 in the equation
∴ y = 20(6) + 200
∴ y = 120 + 200
∴ y = 320
Tom would pay $320 to join Super Fit for 6 months
∵ The cost of Platinum gym = the cost of super Fit
∴ 30x + 90 = 20x + 200
- Subtract 20x from both sides
∴ 10x + 90 = 200
- Subtract 90 from both sides
∴ 10x = 110
- Divide both sides by 10
∴ x = 11
It costs the same amount of money for both gyms after 11 month
For the number of months lass than 11 month Platinum gym is the
better deal
For the number of months greater than 11 month Super Fit is the
better deal
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