# 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* = 0.36*x*

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

**Step 3:**

Sale price = $496 = 0.64*x*

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* = 0.1*x*

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

**Step 3:**

Sale price = $558 = 0.9*x*

Solving for *x*

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

So, original price = $620