Question

Courtney bought a new electric wok that was originally priced at $38. The department store

advertised a rebate of $5 as well as a discount of 25% off all small appliances. Let r(x) = the price
after the rebate and let p(x) = the price after the discount.
Find r(p(x)) and p(r(x)). Which composition will save her the most money?

Answer 1

Let x = the original price of the electric wok.

r(x) = x - $5 (the price after the rebate)

p(x) = x * (1 - 0.25) (the price after the discount)

Given that x = $38, we can substitute that value in to find the final cost of the wok in each composition:

r(p(x)) = r(p(38)) = r(38 * (1 - 0.25)) = r(28.5) = 28.5 - $5 = $23.50

p(r(x)) = p(r(38)) = p(38 - $5) = p(33) = 33 * (1 - 0.25) = $24.75

So, r(p(x)) = $23.50 and p(r(x)) = $24.75

r(p(x)) will save her the most money.