Question

We're saying a 20 percent DISCOUNT, not 20 percent off!!!! so its not (.20)x its actually (.8)x we're also adding on an 8 percent sales tax (if we were taking off 8 percent, we'd write .92) but we're adding an 8 percent sales tax, so we'd write 1.08. so (1.08)(.8)x = p p/(1.08)(.8) = x A) (1.08)(.8)x = p p/(1.08)(.8) = x B) (1.08)(.8)x = p p/(1.08)(.8) = 2x C) (1.08)(.8)x = p p/(1.08)(.8) = 0.5x D) (1.08)(.8)x = p p/(1.08)(.8) = 3x

Answer 1

x = (1.08)(0.8)p, but see possible differences in the definitions of x and p.

Explanation:

Let x be the final price, including sales tax. The first step is to apply the discount to the price, p: to give the discounted price, p'.

p' = 0.8p

Now an 8% sales tax must be added to the discounted price to obtain the final price, x. This can be written as:

x = (1.08)*p'

Substitute the definition of p' [0.8p] to obtain:

x = (1.08)*(0.8p)

x = (1.08)(0.8)p

The answer options don't match exactly, but it is probably due to a difference in definitions of p and x. The derivation above set a as the new price and p as the original price. If this is true, then option A would match.

A) (1.08)(.8)x = p

p/(1.08)(.8) = x

B) (1.08)(.8)x = p

p/(1.08)(.8) = 2x

C) (1.08)(.8)x = p

p/(1.08)(.8) = 0.5x

D) (1.08)(.8)x = p

p/(1.08)(.8) = 3x