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A gym offers three levels of membership based on the number of visits per month, as represented by the table below:

\begin{tabular}{|c|c|c|}
\hline
\begin{tabular}{c}
Max Visits \\
Per Month
\end{tabular} & \begin{tabular}{c}
Cost Per \\
Visit (\[tex]$)
\end{tabular} & \begin{tabular}{c}
Monthly \\
Fee (\$[/tex])
\end{tabular} \\
\hline 12 & 5 & 15 \\
\hline 16 & 4 & 32 \\
\hline 24 & 3 & 42 \\
\hline
\end{tabular}

Kaleigh wants to know how much she will pay for her gym membership. Which graph represents the total monthly cost at the gym as a function of the number of visits Kaleigh plans to make each month?



Answer :

GinnyAnswer
Certainly! Let's analyze how much Kaleigh will pay for her gym membership based on the number of visits she plans to make each month by considering the different membership plans.

### Membership Plans:
1. Plan 1:
- Max Visits: 12
- Cost Per Visit: [tex]$5 - Monthly Fee: $[/tex]15

2. Plan 2:
- Max Visits: 16
- Cost Per Visit: [tex]$4 - Monthly Fee: $[/tex]32

3. Plan 3:
- Max Visits: 24
- Cost Per Visit: [tex]$3 - Monthly Fee: $[/tex]42

### Step-by-Step Solution:

#### For Visits Ranging from 1 to 12:
- If Kaleigh's planned visits fall within this range, she will follow Plan 1.
- The total cost would be calculated as [tex]\((\text{Number of Visits} \times \$5) + \$15\)[/tex].

#### For Visits Ranging from 13 to 16:
- If Kaleigh's planned visits fall within this range, she will switch to Plan 2.
- The total cost would be calculated as [tex]\((\text{Number of Visits} \times \$4) + \$32\)[/tex].

#### For Visits Ranging from 17 to 24:
- If Kaleigh's planned visits exceed 16 but are 24 or less, she will follow Plan 3.
- The total cost would be calculated as [tex]\((\text{Number of Visits} \times \$3) + \$42\)[/tex].

### Cost Analysis for Each Number of Visits:
1. Visits = 1:
- Falls under Plan 1.
- Total Cost = [tex]\(1 \times 5 + 15 = 20\)[/tex].

2. Visits = 2:
- Falls under Plan 1.
- Total Cost = [tex]\(2 \times 5 + 15 = 25\)[/tex].

3. Visits = 3:
- Falls under Plan 1.
- Total Cost = [tex]\(3 \times 5 + 15 = 30\)[/tex].

4. Visits = 4:
- Falls under Plan 1.
- Total Cost = [tex]\(4 \times 5 + 15 = 35\)[/tex].

5. Visits = 5:
- Falls under Plan 1.
- Total Cost = [tex]\(5 \times 5 + 15 = 40\)[/tex].

6. Visits = 6:
- Falls under Plan 1.
- Total Cost = [tex]\(6 \times 5 + 15 = 45\)[/tex].

7. Visits = 7:
- Falls under Plan 1.
- Total Cost = [tex]\(7 \times 5 + 15 = 50\)[/tex].

8. Visits = 8:
- Falls under Plan 1.
- Total Cost = [tex]\(8 \times 5 + 15 = 55\)[/tex].

9. Visits = 9:
- Falls under Plan 1.
- Total Cost = [tex]\(9 \times 5 + 15 = 60\)[/tex].

10. Visits = 10:
- Falls under Plan 1.
- Total Cost = [tex]\(10 \times 5 + 15 = 65\)[/tex].

11. Visits = 11:
- Falls under Plan 1.
- Total Cost = [tex]\(11 \times 5 + 15 = 70\)[/tex].

12. Visits = 12:
- Falls under Plan 1.
- Total Cost = [tex]\(12 \times 5 + 15 = 75\)[/tex].

13. Visits = 13:
- Falls under Plan 2.
- Total Cost = [tex]\(13 \times 4 + 32 = 84\)[/tex].

14. Visits = 14:
- Falls under Plan 2.
- Total Cost = [tex]\(14 \times 4 + 32 = 88\)[/tex].

15. Visits = 15:
- Falls under Plan 2.
- Total Cost = [tex]\(15 \times 4 + 32 = 92\)[/tex].

16. Visits = 16:
- Falls under Plan 2.
- Total Cost = [tex]\(16 \times 4 + 32 = 96\)[/tex].

17. Visits = 17:
- Falls under Plan 3.
- Total Cost = [tex]\(17 \times 3 + 42 = 93\)[/tex].

18. Visits = 18:
- Falls under Plan 3.
- Total Cost = [tex]\(18 \times 3 + 42 = 96\)[/tex].

19. Visits = 19:
- Falls under Plan 3.
- Total Cost = [tex]\(19 \times 3 + 42 = 99\)[/tex].

20. Visits = 20:
- Falls under Plan 3.
- Total Cost = [tex]\(20 \times 3 + 42 = 102\)[/tex].

21. Visits = 21:
- Falls under Plan 3.
- Total Cost = [tex]\(21 \times 3 + 42 = 105\)[/tex].

22. Visits = 22:
- Falls under Plan 3.
- Total Cost = [tex]\(22 \times 3 + 42 = 108\)[/tex].

23. Visits = 23:
- Falls under Plan 3.
- Total Cost = [tex]\(23 \times 3 + 42 = 111\)[/tex].

24. Visits = 24:
- Falls under Plan 3.
- Total Cost = [tex]\(24 \times 3 + 42 = 114\)[/tex].

### Summarizing the Costs:
Here's how the costs align with the visits:

- Visits: 1 to 12 → Costs: [tex]$20, $[/tex]25, [tex]$30, $[/tex]35, [tex]$40, $[/tex]45, [tex]$50, $[/tex]55, [tex]$60, $[/tex]65, [tex]$70, $[/tex]75.
- Visits: 13 to 16 → Costs: [tex]$84, $[/tex]88, [tex]$92, $[/tex]96.
- Visits: 17 to 24 → Costs: [tex]$93, $[/tex]96, [tex]$99, $[/tex]102, [tex]$105, $[/tex]108, [tex]$111, $[/tex]114.

These costs tell us how much Kaleigh will pay each month based on the number of visits she plans to make.

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