To determine the best payment option for different scenarios, let’s analyze each situation based on the cost of visiting the amusement park.
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You have plans to attend 3 times this summer.
- Pay per visit: \(3 \times 28 = 84\)
- Membership: \(90 + (3 \times 15) = 90 + 45 = 135\)
- Answer: Pay per visit
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You think you will visit probably about 8 times this summer.
- Pay per visit: \(8 \times 28 = 224\)
- Membership: \(90 + (8 \times 15) = 90 + 120 = 210\)
- Answer: Buy a membership
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You have budgeted $150 for visiting the park this summer.
- Pay per visit: You cannot visit more than \( \frac{150}{28} \approx 5.36\), so at most 5 visits, costing \(5 \times 28 = 140\).
- Membership: \(90 + (4 \times 15) = 90 + 60 = 150\) (5 visits can be achieved with a membership).
- Answer: Buy a membership
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How many visits would be approximately the break-even point where both options would cost about the same?
- Pay per visit cost = \(28x\)
- Membership cost = \(90 + 15x\)
- Set them equal to find the break-even point: \[ 28x = 90 + 15x \] \[ 28x - 15x = 90 \] \[ 13x = 90 \] \[ x \approx 6.92 \]
- Rounding gives approximately 7 visits to reach the break-even point.
- Answer: 7 visits (This value changes based on the options given)
So, based on your given options and my calculations:
- 3 visits: Pay per visit
- 8 visits: Buy a membership
- Budget of $150: Buy a membership
- Break-even point: 7 visits.
If we were estimating 5 visits as a nearby option based on rounding, it can be adjusted towards the provided options.
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