An amusement park that you are excited to try is $28 per visit.
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
To find the break-even point where both options would cost about the same, we need to solve the equation:
$90 + $15x = $28x
where x represents the number of visits.
Simplifying the equation, we get:
$90 = $28x - $15x
$90 = $13x
To solve for x, we divide both sides of the equation by $13:
x = $90 / $13
x ≈ 6.923
Therefore, at approximately the seventh visit, both options would cost about the same.
To find the break-even point, we need to calculate the number of visits that would make both options cost approximately the same amount.
Let's assume the break-even point is x visits.
For the monthly membership option:
Total cost = Monthly membership cost + (Number of visits * Cost per visit)
Total cost = $90 + (x * $15)
For the one-time visit option:
Total cost = Number of visits * Cost per visit
Total cost = x * $28
Since we want the two options to cost about the same:
$90 + (x * $15) = x * $28
Now, let's solve this equation for x:
$90 + $15x = $28x
Subtract $15x from both sides:
$90 = $28x - $15x
Combine like terms:
$90 = $13x
Divide both sides by $13:
$90 / $13 = x
x ≈ 6.923
Since x represents the number of visits, we cannot have a fraction of a visit. So, rounding up, the approximate break-even point is 7 visits. At 7 visits, both options would cost approximately the same amount.
To find the break-even point where both options would cost about the same, we need to determine the number of visits at which the total cost of each option is equal.
For the pay-per-visit option, the cost per visit is $28.
For the monthly membership option, there is an upfront cost of $90, and each visit costs an additional $15.
Let's calculate the break-even point using a formula:
Total Cost for Pay-per-Visit Option = Total Cost for Monthly Membership Option
Number of Visits * Cost per Visit = Membership Cost + (Number of Visits * Cost per Visit for Membership)
Using this formula and simplifying the equation, we can solve for the number of visits:
Number of Visits * $28 = $90 + (Number of Visits * $15)
Rearranging the equation, we get:
(Number of Visits * $28) - (Number of Visits * $15) = $90
Combining like terms:
Number of Visits * ($28 - $15) = $90
Number of Visits * $13 = $90
Dividing both sides by $13:
Number of Visits = $90 / $13
Number of Visits ≈ 6.92
Since the number of visits cannot be a fraction of a visit, we can round up to the nearest whole number.
Therefore, the break-even point is approximately 7 visits.