Graphing Application of Systems of equations: Gym Comparison

2 Slides • 8 Questions

1

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.

2

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?

1

$y=20+1.5x$

$y=5+4x$

2

$y=20x+1.5$

$y=5x+4$

3

$y=1.5x+20$

$y=5x+4$

4

$y=1.5+20x$

$y=5+4x$

3

Multiple Choice

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

y = 20 + 1.5x

1

$0 & $15

2

$20 & $35

3

$1.50 & $20

4

$5 & $45

4

Multiple Choice

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

y = 5 + 4x

1

$4 & $44

2

$20 & $35

3

$5 & $37

4

$0 & $8

5

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).

Type response here

6

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

7

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.

8

Math Response

x = 6, solve for y.

$y=20+1.5x$

$y=5+4x$

Type answer here

Deg^°

Rad

9

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.

1

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

2

The cost for 29 visits is 6 dollars.

3

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

4

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

10

Multiple Choice

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

(Hint: use your graph)

1

Alice's Athletic Arena

2

Jim's Gym

3

The cost would be the same at either gym.

4

Not enough information

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.

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