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