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

Step 1:

Let the original price be = x

Discount rate = 36%

Step 2:

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

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

Step 3:

Sale price = $496 = 0.64x

Solving for x

x = $frac{496}{0.64} =$ $775

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

Step 1:

Let the original price be = x

Discount rate = 10%

Step 2:

Discount = 10% of x = 0.10 × x = 0.1x

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

Step 3:

Sale price = $558 = 0.9x

Solving for x

x = $frac{558}{0.9} =$ $620

So, original price = $620