Question

A store offers a rewards program where shoppers earn 1 point for every $5 they spend plus 100 bonus points on their first purchase. If function f represents the number of points earned as a function of the total amount spent x, which function represents the total amount spent as a function of the number of points earned?

Answer 1

The expression that represents the total amount spent as a function of the number of points earned is x = y*5 - 500. This function is only valid for 100 or plus points, since that is the minimum amount of one can have after a purchase.

Explanation:

To solve this problem we will first calculate the function that relates the number of points earned and the total spent x. This is given by:

y = f(x) = 100 + x/5

In order to calculate the function that represents the total spent as a function of points earned we need to isolate the variable x, in the expression above. We have:

y = 100 + x/5

y - 100 = x/5

x/5 = y - 100

x = y*5 - 500

The expression that represents the total amount spent as a function of the number of points earned is x = y*5 - 500. This function is only valid for 100 or plus points, since that is the minimum amount of points one can have after a purchase.