Question

A manager at a clothing store is determining the retail prices of items so that they can be tagged and placed on the sales floor. The equation that the manager uses is R = C + MC where R is the retail price, C is the cost that the store pays for the item, and M is the percent (expressed as a decimal) that the item is marked up. a. The markup for women's athletic shoes is 40%. Write a function that gives the retail price R in terms of the cost C. b. Find the inverse of the function from part (a). c. Use the inverse function to find the cost of a pair of women's athletic shoes that has a retail price of $60

Answer 1

The function for the retail price R of women's athletic shoes in terms of the cost C is R = 1.40C, with a markup of 40%. The inverse function is C = R/1.40. Using the inverse function, the calculated cost of women's athletic shoes at a retail price of $60 is approximately $42.86.

Step-by-step explanation:

The manager at the clothing store uses the equation R = C + MC to set the retail prices, where R is the retail price, C is the cost to the store, and M is the markup percentage in decimal form.

Part a: Function for Retail Price R in Terms of Cost C

Given the markup for women's athletic shoes is 40%, we represent this as M = 0.40. The function that gives the retail price R in terms of the cost C is R = C + 0.40C, which simplifies to R = 1.40C.

Part b: Inverse of the Function

To find the inverse of the function, we solve for C in terms of R. Starting with R = 1.40C, we divide both sides by 1.40 to obtain C = R/1.40, which is the inverse function.

Part c: Finding the Cost Using the Inverse Function

A retail price of $60 for a pair of women's athletic shoes means we use the inverse function C = R/1.40.

Substituting R with $60 gives C = $60 / 1.40.

Therefore, the cost of the shoes for the store is approximately $42.86.