an amusement park that you are excited to try is 28$ per visit. you have the option to purchase a monthly membership of 90$ and then pay $15 for each visit. how many visits would break the even point where both options would cost about the same

Question

an amusement park that you are excited to try is 28$ per visit. you have the option to purchase a monthly membership of 90$ and then pay $15 for each visit. how many visits would break the even point where both options would cost about the same

Answer 1

To find the break-even point, we need to equate the cost of the two options.

Let's assume the number of visits required to reach the break-even point is 'x'.

Option 1:
Cost per visit = $28
Number of visits = x
Total cost = 28x

Option 2:
Membership cost = $90
Cost per visit = $15
Number of visits = x
Total cost = 90 + 15x

Setting both options equal to each other:
28x = 90 + 15x

Rearranging the equation:
28x - 15x = 90
13x = 90

Dividing both sides by 13:
x = 90/13 ≈ 6.92

Since we can't have a fraction of a visit, we need to round up to the nearest whole number. Therefore, it would take at least 7 visits to break even between the two options.

Answer 2

To determine the breakeven point where both options cost about the same, we need to set up an equation and solve for the number of visits.

Let's assume the number of visits required to break even is "x".

Option 1 (Pay per visit):
Cost per visit = $28
Total cost for x visits = 28x

Option 2 (Monthly membership):
Monthly membership cost = $90
Cost per visit = $15
Total cost for x visits = 90 + 15x

Setting the two options equal to each other:
28x = 90 + 15x

Simplifying the equation:
28x - 15x = 90
13x = 90

Dividing both sides by 13:
x = 90/13

Calculating the value:
x ≈ 6.92

Therefore, to break even, you would need to visit the amusement park approximately 7 times.

Answer 3

To determine the break-even point where both options would cost about the same, we need to compare the total cost of multiple visits using the individual visit price to the cost of purchasing the monthly membership and paying per visit.

Let's use the variable 'x' to represent the number of visits.

For the first option, where each visit costs $28:
Total cost = $28 * x

For the second option, where there is a monthly membership fee of $90 and each visit costs $15:
Total cost = $90 + ($15 * x)

We need to find the value of 'x' that makes both total costs equal.

Setting the two equations equal to each other:

$28 * x = $90 + ($15 * x)

Now, let's solve for 'x'.

$28x = $90 + $15x

Subtract $15x from both sides:

$13x = $90

Divide both sides by $13:

x = $90 / $13

x ≈ 6.92

So, approximately 6.92 visits would be the break-even point where both options would cost about the same. Since you cannot have a fraction of a visit, you would need to round up to the nearest whole number, which means you would need to visit the amusement park 7 times to make both options cost about the same.