Finding the original price given the sale price and percent discount

In this lesson, we learn how to find the original price, given the sale price and percent discount.

**Rules to find the original price given the sale price and percent discount**

First consider the unknown original price as ‘*x*’.

Then consider the rate of discount.

To find the actual discount, multiply the discount rate by the original amount ‘*x*’.

To find the sale price, subtract the actual discount from the original amount ‘*x*’ and equate this to given sale price.

Solve the equation and find the original amount ‘*x*’.

A desk is being sold at a 36% discount. The sale price is $496. What was its original price?

#### Solution

Let the original price be = *x*

Discount rate = 36%

Discount = 36% of *x* = 0.36 × *x* = 0.36*x*

Sale price = Original price − Discount = *x* − 0.36*x* = 0.64*x*

Sale price = $496 = 0.64*x*

Solving for *x*

So, original price = $775

If a Play Station was bought for $558 after a 10% discount, what was the original price of the Play Station?

#### Solution

Let the original price be = *x*

Discount rate = 10%

Discount = 10% of *x* = 0.10 × *x* = 0.1*x*

Sale price = Original price − Discount = *x* − 0.1*x* = 0.9*x*

## 1/6 off 150 dollars

If something costs $150 and is on sale for 1% off, then how much would it cost? Here we will show you how to calculate how much you save (discount) and how much you have to pay if something you want to buy is regularly $150, but is currently on sale for 1 percent off.

There are many ways of calculating your discount and final purchase price. One way is to multiply 150 dollars by 1 percent, and then divide the answer by one hundred, then deduct that result from the original price. See illustration below:

$150 SALE 1% OFF |

**Purchase Price:**

$150

$150

**Discount:(150 x 1)/100 = $1.50**

**Final Price:150 – 1.50 = $148.50**

Thus, a product that normally costs $150 with a 1 percent discount will cost you $148.50, and you saved $1.50.

You can also calculate how much you save by simply moving the period in 1.00 percent two spaces to the left, and then multiply the result by $150 as follows: $150 x .01 = $1.50 savings.

Furthermore, you can get the final price by simply deducting .01 from 1 and multiplying it by $150 as follows: (1 – .01) x $150 = $148.50 final price.

**Percent Off Calculator**

Go here to take a percent discount off another amount.

**What is 1 percent off 151 dollars?**

Go here for our next percent off dollar calculation.