To determine whether purchasing the monthly membership is a better option than paying per visit, we can set up the equations based on your usage.
Option A: Pay per visit. The cost function is: \[ y = 9x \] where \( y \) is the total cost and \( x \) is the number of visits.
Option B: Monthly membership. The cost function is: \[ y = 30 + 4x \] where \( y \) is the total cost and \( x \) is the number of visits.
Now, we can compare the two cost functions to find the break-even point, which is when both costs are equal:
\[ 9x = 30 + 4x \]
To solve for \( x \):
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Subtract \( 4x \) from both sides: \[ 9x - 4x = 30 \] \[ 5x = 30 \]
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Divide by 5: \[ x = 6 \]
This means that if you plan to visit the trampoline park more than 6 times in a month, the membership option will be cheaper.
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If you visit 6 times:
- Option A: \( 9 \times 6 = 54 \)
- Option B: \( 30 + 4 \times 6 = 30 + 24 = 54 \) (break-even)
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If you visit 7 times:
- Option A: \( 9 \times 7 = 63 \)
- Option B: \( 30 + 4 \times 7 = 30 + 28 = 58 \) ( membership is cheaper)
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If you visit 5 times:
- Option A: \( 9 \times 5 = 45 \)
- Option B: \( 30 + 4 \times 5 = 30 + 20 = 50 \) (pay per visit is cheaper)
Given this analysis, it would make sense to buy the membership if you plan to visit more than 6 times in a month. If you anticipate using the trampoline park less than or equal to 6 times, then it would be more cost-effective to pay the regular fee of $9 per visit.
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