To evaluate the best option for visiting the amusement park, we need to compare the costs of the single visit option to the monthly membership option based on the number of visits.
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For 3 visits:
- Single visit cost: \( 3 \times 28 = 84 \)
- Monthly membership cost: \( 90 + (15 \times 3) = 90 + 45 = 135 \)
- Which option is best? Single visit option
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For 8 visits:
- Single visit cost: \( 8 \times 28 = 224 \)
- Monthly membership cost: \( 90 + (15 \times 8) = 90 + 120 = 210 \)
- Which option is best? Monthly membership option
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For a budget of $150:
- Single visit cost for maximum visits:
- \( 150 \div 28 \approx 5.36 \), so 5 visits would cost \( 5 \times 28 = 140 \) (under budget).
- Monthly membership cost: \( 90 + (15 \times 4) = 90 + 60 = 150 \) (exactly at budget).
- Which option is best? Monthly membership option (because you can visit 5 times with the single visit and 4 times with membership, but all 4 visits can be made).
- Single visit cost for maximum visits:
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For the break-even point:
- Let \( x \) be the number of visits.
- Cost of single visits: \( 28x \)
- Cost of membership: \( 90 + 15x \)
- Set the two expressions equal: \[ 28x = 90 + 15x \] \[ 28x - 15x = 90 \] \[ 13x = 90 \] \[ x = \frac{90}{13} \approx 6.92 \]
- The break-even point is about 7 visits.
Therefore, the responses are:
- Which option is best for 3 visits? Single visit option
- Which option is best for 8 visits? Monthly membership option
- Which option is best for a budget of $150? Monthly membership option
- How many visits would be approximately the break-even point? 7 visits