algebra question

Question

Jane bought a pair of headphones at a 20% discount. After including the 8% sales tax, the total

price of the headphones was $54. What was the original price of the headphones before the

discount?

Answer 1

Let the original price of the headphones be =100

after 20%discount the new price = 100- 20% of 100 = 100 - 20 =80

after 8% sales tax the final price = 80+ 8% of 80 = 80 + 6.4 = 86.4

As it is given that the final price = 54

now

original price final price

100 86.4

X 54

Hence

X ∗ 86.4 = 100 ∗ 54 ( by cross multiplication)

X = 100 ∗ 54 ⁄ 86.4 = $ 62.50

Answer 2

work backwards

what was the price before the sales tax was added ?

108% of what number is $54 ?

1.08*P=54

P=54/1.08

P=$50

now, what was the original price before 20% was taken off ?

if there is a 20% discount that means you paid only 80% of the original price

80% of what number is $50 ?

0.8*P=50

P=50/0.8

P=$62.50 was the original price