# Finding the original amount given the result of a percentage increase or decrease

In this lesson, we learn how to find the original amount, given result of a percent increase or decrease.

Rules to find the original amount given the result of a percentage increase or decrease

• First consider the unknown original amount as ‘x’.

• Then consider the percent rate of increase or decrease

• To find the increase or decrease, multiply the rate by the original amount ‘x’.

• To find the final amount, add or subtract the increase or decrease to the original amount ‘x’ and equate this to given final amount.

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

After a 25% increase, a TV was $750. Find the original price ### Solution Step 1: Let the original amount be = x Percent increase = 25% Step 2: Increase in price = 25% of x = 0.25 × x = 0.25x Final amount = Original amount + increase = x + 0.25x = 1.25x Step 3: Final amount =$750 = 1.25x

Solving for x

x = $\frac{750}{1.25} =$ $600 So, original amount =$600

After a 60% discount, a lawn chair was $105. Find the original price ### Solution Step 1: Let the original amount be = x Percent increase = 60% Step 2: Decrease in price = 60% of x = 0.60 × x = 0.6x Final amount = Original amount − Decrease = x − 0.6x = 0.4x Step 3: Final amount =$105 = 0.4x

Solving for x

x = $\frac{105}{0.4} =$ $262.50 So, original amount =$262.50