Tom and his best friend are going to join a gym. 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. write an equation that shows the membership cost for each gym (2 points). if tom joins platinum gym, how much would it cost for 6 months? (1 point) how much would it cost for tom to join super fit? (1 point) how many months until it costs the same amount of money for both gyms? (2 points-show your work) which gym deal is a better deal? (2 points for explaining)

Part 1:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2:  $270

Part 3:  $320

Part 4:  11 months

Part 5:  See explanation below

Step-by-step explanation:

Part 1:

Let "x" be the number of months:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2:

We put x = 6 in platinum gym's equation and get our answer.

90 + 30x

90 + 30(6)

90 + 180

=$270

Part 3:

We put x = 6 into super fit's equation and get our answer.

200 + 20x

200 + 20(6)

200 + 120

=$320

Part 4:

To find the number of months for both gyms to cost same, we need to equate both equations and solve for x:

90 + 30x = 200 + 20x

10x = 110

x = 11

So 11 months

Part 5:

We know for 11 months, they will cost same. Let's check for 10 months and 12 months.

In 10 months:

Platinum = 90 + 30(10) = 390

Super Fit = 200 + 20(10) = 400

In 12 months:

Platinum = 90 + 30(12) = 450

Super Fit = 200 + 20(12) = 440

Thus, we can see that Platinum Gym is a better deal if you want to get membership for months less than 11 and Super Fit is a better deal if you want to get membership for months greater than 11.

step-by-step explanation:

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.