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)

The equation that shows the membership cost for Platinum gym isy = 30x + 90The equation that shows the membership cost for Super Fit isy = 20x + 200Tom would pay $270 to join Platinum gym for 6 monthsTom would pay $320 to join Super Fit for 6 monthsIt costs the same amount of money for both gyms after 11 monthFor the number of months lass than 11 month Platinum gym is the better dealFor the number of months greater than 11 month Super Fit is the better dealStep-by-step explanation:Tom saw that Platinum gym has a sale with a one time fee of $90 and a monthly fee of $30Tom's friend sees that Super Fit only charges $20 a month, but its registration fee is $200To write an equation that shows the membership cost for each gymdo that:1. Assume that the number of months for the membership is x2. Assume that the cost for the membership in x month is y3. 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 + 90The equation that shows the membership cost for Platinum gym isy = 30x + 90Super 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 + 200The equation that shows the membership cost for Super Fit isy = 20x + 200∵ Tom joins Platinum gym for 6 months∴ x = 6∵ y = 30x + 90To find the cost of the 6 months substitute x by 6 in the equation∴ y = 30(6) + 90∴ y = 180 + 90 ∴ y = 270Tom would pay $270 to join Platinum gym for 6 months∵ Tom joins Super Fit for 6 months∴ x = 6∵ y = 20x + 200To find the cost of the 6 months substitute x by 6 in the equation∴ y = 20(6) + 200∴ y = 120 + 200 ∴ y = 320Tom 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 = 11It costs the same amount of money for both gyms after 11 monthFor the number of months lass than 11 month Platinum gym is the better dealFor the number of months greater than 11 month Super Fit is the better dealLearn more:You can learn more about equation in brainly.com/question/8955867#LearnwithBrainly