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