Hi, there--

The Problem:
The sale price of a coffeemaker is $40.08. This is 40% off the original price. What was the original
price of the coffeemaker? 

A Solution:
The sale price of an item is equal to the original price less the discounted amount. In this case we have
a 40% discount.

Let x be the original price of the coffee maker.
The discount rate is 40%. To find the discounted amount, first convert 40% to its decimal
representation: 40% = 0.40 
The dollar amount of the discount is the discount rate times the original price, or 0.40*x.

The sale price is the original price minus the dollar amount of the discount, or
[sales price] = [original price] - [dollar amount of discount]
In algebra, this is
40.08 = x - 0.4x
.
We solve for x to find the original price of the coffee maker. Combine like terms.
40.08 = 0.60x

Divide both sides of the equation by 0.60.
40.08/0.60 = x
x = 66.80

The original price of the coffee maker was $66.80.

Feel free to email if you have questions about this solution.

Ms.Figgy
math.in.the.vortex@gmail.com