Let's compare the two options based on the number of visits.
- Cost of Pay per visit: $28 per visit
- Cost of Monthly Membership: $90 + $15 per visit.
Let's calculate the cost for each option based on different visit scenarios:
1. Plans to attend 3 times:
- Pay per visit cost: \( 3 \times 28 = 84 \)
- Membership cost: \( 90 + (3 \times 15) = 90 + 45 = 135 \)
Best option for 3 visits: Pay per visit ($84) is cheaper.
2. Plans to visit 8 times:
- Pay per visit cost: \( 8 \times 28 = 224 \)
- Membership cost: \( 90 + (8 \times 15) = 90 + 120 = 210 \)
Best option for 8 visits: Membership ($210) is cheaper.
3. Budget of $150:
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Pay per visit cost for a budget of 150:
- Number of visits \( = \frac{150}{28} \approx 5.36 \), so 5 visits max.
- Total cost for 5 visits: \( 5 \times 28 = 140 \)
-
Membership cost:
- Tried until $150 budget: The maximum number of visits = \( 150 - 90 = 60 \) but only if cost is per visit \( 15 \), so \( \frac{60}{15} = 4 \times \)
Thus, you can buy membership and visit 4 times, the total cost is $90 + ($15 * 4) = $90 + $60 = $150 which exactly meets the budget.
Best option within the budget: Both memberships with 4 visits and pay-per-visit with 5 visits will fit in, so calculate which is ideal based on the visits assumed.
Break-even Point:
To find the break-even point, set the costs equal:
\[ 28n = 90 + 15n \]
Where \( n \) is the number of visits.
Solving for \( n \): \[ 28n - 15n = 90 \] \[ 13n = 90 \] \[ n \approx 6.92 \quad (or\ 7) \]
Therefore, the break-even point is approximately 7 visits.
Summary of options:
- For 3 visits: Best option is pay per visit ($84).
- For 8 visits: Best option is membership ($210).
- For $150 budget: Both options can be made to fit but membership covers at least 4 visits.
- Break-even point: Approximately 7 visits.