Question

Two new rides are being compared by a local amusement park in terms of their annual operating costs. The two rides would generate the same level of revenue (thus the focus on costs).

The Tummy Tugger has fixed costs of $10,000 per year and variable costs of $2.50 per visitor.
The Head Buzzer has fixed costs of $4,000 per year and variable costs of $4.00 per visitor.
Mathematically find the number of visitors per year for the two rides to have equal annual costs.

Answer 1

To find the number of visitors per year for the two rides to have equal annual costs, we need to set up and solve an equation. The two rides will have equal annual costs when there are 4,000 visitors per year.

Step-by-step explanation:

To find the number of visitors per year for the two rides to have equal annual costs, we need to equate the total costs of each ride. The total cost is the sum of the fixed costs and the variable costs. Let x represent the number of visitors. For the Tummy Tugger ride, the total cost is $10,000 (fixed cost) plus $2.50 (variable cost) multiplied by x. For the Head Buzzer ride, the total cost is $4,000 (fixed cost) plus $4.00 (variable cost) multiplied by x. Setting these two equations equal to each other, we get:

$10,000 + $2.50x = $4,000 + $4.00x

Now we can solve for x:

$10,000 - $4,000 = $4.00x - $2.50x

$6,000 = $1.50x

x = $6,000/$1.50 = 4,000

Therefore, the two rides will have equal annual costs when there are 4,000 visitors per year.