College Algebra

Question

You plan to join a gym near your new home. Universe Fitness will charge you $100/year plus an additional $1.50 per fitness class you attend. Silver's Gym charges $150/year but only $1 per fitness class.

Part 1 of 3: (2 pts)

Write a model representing the cost of Universe Fitness, U(x), if you attend x fitness classes.

Part 2 of 3: (2 pts)

Write a model representing the cost of Silver's Gym, S(x), if you attend x fitness classes

Part 3 of 3: (4 pts)

Find the number of fitness class you would need to attend in a year for the cost of both gyms to be the same. What would be the cost of using either gym at that point? Show all work using the equation editor. Find your answer ALGEBRAICALLY. Be sure to write a sentence that explains your answer.

Answer 1

Part 1

U(x)=1.5x+100

part 2

S(x)=1.0x+150

Part 3

1.5x+100=1.0x+150 subtract 100 from both sides

1.5x+100-100=1.0x+150-100

1.5x=1.0x+50 subtract 1.0x from each side

1.5x-1.0x-=1.0x-1.0x+50

0.5x=50 divide by 0.5

0.5x/0.5=50/0.5

x=100

1.5(100)+100=250

The gym memberships will be the same when 100 classes are taken. The cost of the gyms with 100 classes in a year is $250.00.

Answer 2

x = number of fitness classes.

Part 1: U(x) = 100 + 1.50x

Part 2: S(x) = 150 + x

Part 3: 100 + 1.5x = 150 + x

0.5x = 50

x =100 100 classes

150+ 100 = 250 $250 to attend each gym.