Jane paid $40 for an item she received a 20% discount. Janes friend says this means that the original price of the item was $48

Jane's friend is wrong. The original price was $50

Step-by-step explanation:

Jane got a 20% discount, so she paid 80% of the original price. As a ratio she paid

80% : 100% = 80/100 = 4/5

She paid four fifths the regular price, so we can set up an equation to find out what that price was.

(4/5) x = 40 (four-fifths of some value is 40)

now solve for x

multiply both sides by 5 to get rid of the fraction ...

4x = 200

divde both sides by 4 to isolate x

x = 50

$50 was the original price