Graphing Application of Systems of equations: Gym Comparison

By Jennifer Ferrara

​Alice's Athletic Arena vs Jim's Gym

​Alice's Athletic Arena requires members to pay $20 to join for a month and $1.50 each time they visit to work out.



Jim's Gym requires members to pay $5 to join for a month and $4 each time they visit to work out.

Multiple Choice

Alice’s Athletic Arena: $20/month & $1.50/visit

Jim’s Gym : $5/month & $4/visit

Which system of equations represents the cost for one month at each gym?

 

• $$y=20+1.5x$$  

  $$y=5+4x$$  

• $$y=20x+1.5$$  

  $$y=5x+4$$  

• $$y=1.5x+20$$  

  $$y=5x+4$$  

• $$y=1.5+20x$$  

  $$y=5+4x$$  

Multiple Choice

Calculate the total cost for 0 & 10 visits in a month at Alice's Arena.

y = 20 + 1.5x

• $0 & $15

• $20 & $35

• $1.50 & $20

• $5 & $45

Multiple Choice

Calculate the total cost for 0 & 8 visits in a month to Jim's Gym?

y = 5 + 4x

• $4 & $44

• $20 & $35

• $5 & $37

• $0 & $8

Open Ended

Graph the system of equations on the grid provided using the table of values for each equation. Use a ruler.

Estimate the point of intersection (x , y).

​Check your solution algebraically

Substitute the variables in each equation of the system with the values from YOUR point of intersection (x, y).

Alice's Athletic Arena Jim's Gym
y = 20 + 1.50x y = 5 + 4x

Poll

Is your estimate the solution to the system of equations?

Explain.

•  

   Yes, my estimate is a solution BOTH equations.

•  

   No, my estimate was a solution for only ONE of the equations.

•  

   No, my estimate was not a solution for either of the equations.

Math Response

x = 6, solve for y.

$$y=20+1.5x$$

  $$y=5+4x$$

Type answer here

Correct Answer: 29

Deg^°

Rad

Multiple Choice

The intersection point on the graph is : $$\left(6,29\right)$$  

Interpret the real-world meaning of the intersection point on the graph.

• The cost for 6 visits is $29 at both gyms.

• The cost for 29 visits is 6 dollars.

• The cost for 6 visits is $29 at Alice's arena only.

• The cost for 6 visits is $29 at Jim's gym only.

Multiple Choice

If you plan on working out more than 6 times per month, which gym would cost less?

(Hint: use your graph)

• Alice's Athletic Arena

• Jim's Gym

• The cost would be the same at either gym.

• Not enough information