Question

1. Tom and his best friend Edward are seeking to join a gym. Tom saw on television that Platinum Gym was having a grand opening in a few months. Tom is considering a membership at Platinum Gym. Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month. Tom's best friend Edward says he plans to join Super Fit because Super Fit only charges $10 a month but has a one-time registration fee of $150.
(a) Write an expression to represent the membership cost of Platinum Gym for x months.


(b) Write an expression to represent the membership cost of Super Fit for x months.


( c) If Tom decides to join Platinum Gym and Edward joins Super Fit, who would pay less during the first month of membership? Who would pay less after a year of membership? Show your work.






(d) Is there a membership period for which Tom and Edward would pay the same amount? If so, how long would this membership be and how much would it cost? Show your work.






(e) Which gym membership is a better deal? Explain why.

Answer 1

A) let x=months let y=cost y=mx+b y= 20x+ 60 Remember 20 is the variable which means in this case every month it cost 20$ and 60 is the constant which means you only pay it once

B) let x= Months let y= cost y=10x + 150

C) platinum gym y= 20x+60 y=20(1)+60 y=20+60 y=80 Superfit y=10x+150 y=10(1)+150 y=10+150 y=160 Therefore Tom will pay less after the first month

D) y=y solve for x y=20x+60 y=10x+150 20x+60=10x+150 -10x. -10x 10x+ 60=150 -60. -60 10x=90 10x/10=90/10 X=9 9 months Pick any equation and sub in x Y=10x+150 Y=10(9)+150 Y=90+150 Y=240 240$ Know that you only have to do one equation to find y but if you want to show both you can Therefore there is a period where Tom and Edward paid the same amount, after nine months they would both pay $240

E) if they plan on going to the gym 9 months and less the best deal gym is platinum gym but if they want to go for more then 9 months then the best deal gym is super fit