An amusement park that you are excited to try is $28 per visit.

Question

You have the option to purchase a monthly membership for $90 and then pay $15 for each visit.

How many visits would be approximately the break even point where both options would cost about the same?

Answer 1

To find the break-even point, we need to set up equations to represent the total cost for each option based on the number of visits.

1. Cost for single visits: \[ \text{Cost}_{\text{single}} = 28 \cdot x \] where \( x \) is the number of visits.

2. Cost for the monthly membership: \[ \text{Cost}_{\text{membership}} = 90 + 15 \cdot x \]

To find the break-even point, we set the two cost equations equal to each other: \[ 28x = 90 + 15x \]

Now, we will solve for \( x \):

1. Subtract \( 15x \) from both sides: \[ 28x - 15x = 90 \] \[ 13x = 90 \]

2. Divide both sides by 13: \[ x = \frac{90}{13} \approx 6.92 \]

Since the number of visits must be a whole number, we can round \( 6.92 \) to either 6 or 7 visits.

• Calculating costs for 6 visits:

  • Single visits: \( 28 \cdot 6 = 168 \)
  • Membership: \( 90 + 15 \cdot 6 = 90 + 90 = 180 \)

• Calculating costs for 7 visits:

  • Single visits: \( 28 \cdot 7 = 196 \)
  • Membership: \( 90 + 15 \cdot 7 = 90 + 105 = 195 \)

Thus, at 6 visits, the membership is more expensive, while at 7 visits, the membership becomes less expensive.

Therefore, the approximate break-even point is at 7 visits. Beyond this point, the monthly membership becomes the more cost-effective option.