Question

2. Mercury High School is requiring students to purchase parking permits this year in order to

use campus parking lots. It costs the school a one-time fee of $500 to have the logo

designed. It also costs $2 per permit to print and cut out each one. They expect the average

cost of each permit to be $6.

a. Write a rational equation that describes the situation above.

b. How many parking permits does Mercury High School need to sell in order for the

average cost of a student's parking permit to be $6? Solve your equation from part (a)

to answer the question. Justify your solution as it relates to the context.

Answer 1

a. $6 = ($500 + $2q) / q

b. 125

Average cost = ($500 + $2q) / q

($500 + $2x 125) / 125 = $6

Explanation:

Average cost = total cost / quantity produced

total cost = fixed cost + variable cost

Fixed costs are costs that do not vary with output. e.g. the cost of the logo

Variable costs are costs that vary with production e.g. cost of printing and cutting

Variable cost = $2 x quantity of parking ticket sold

let q = quantity of parking ticket sold

variable cost = 2q

$6 = ($500 + $2q) / q

to determine the number of parking ticket to be sold for average cost to be $6, take the following steps

Multiply both sides of the equation by q

6q = 500 + 2q

collect like terms

6q - 2q = 500

4q = 500

q = 125

125 tickets have to be sold for average cost to the $125

to justify the answer, replace 125 in the first equation to confirm if $6 would gotten as the average cost

($500 + $2q) / q

($500 + $2x 125) / 125 = $6