Percent of Change

Percent of Change

How to solve percent of change problems (increase, decrease): formula, examples, and their solutions.

Formula

(percent of change) = [(new) - (original)]/(original) *100(%)

(percent of change)
= [(new) - (original)] / (original) × 100%.

100% is multiplied to make the unit % (percent).

The numerator, (new) - (original),
is the amount of change.

So the percent of change
is the ratio of (change)/(original).

Ratio

Example 1: Percent of Increase

For the given data below, find the percent of change. $15 -> $21

First write
the original value ($15) and the new value ($21).

Put the written numbers (15, 21)
into the (% of change) formula.

Reduce 6 to 2.
(6 ÷ 3 = 2)

And reduce 15 to 5.
(15 ÷ 3 = 5)

Reduce 100 to 20.
(100 ÷ 5 = 20)

And cancel the denominator 5.
(5 ÷ 5 = 1)

You got 40%, which is (+).

So [40% of increase] is the answer.

If the calculated result is (+),
the it shows the percent of increase.

Example 2: Percent of Decrease

For the given data below, find the percent of change. $25 -> $22

First write
the original value ($25) and the new value ($22).

Put the written numbers (25, 22)
into the (% of change) formula.

Reduce 100 to 4.
(100 ÷ 25 = 4)

And cancel the denominator 25.
(25 ÷ 25 = 1)

You got -12%, which is (-).

So [12% of decrease] is the answer.

If the calculated result is (-),
the it shows the percent of decrease.

Example 3

If the given data shows 25% of increase, find the value of x. 8 -> x

First write
the original value (8) and the new value (x).

Put the written numbers (8, x)
into the (% of change) formula.

Then it's time to solve this equation.

Linear equations (one variable)

Divide both sided by 25.

Reduce 8 to 2.
(8 ÷ 4 = 2)

And cancel 4.
(4 ÷ 4 = 1)

Multiply both sides by 2.

Move -8 to the right side.

Then x = 2 + 8
= 10.

Example 4

If the given data shows 30% of decrease, find the value of x. x -> 14

First write
the original value (x) and the new value (14).

Put the written numbers (x, 14)
into the (% of change) formula.

Then solve this equation.

Linear equations (one variable)

Divide both sided by 10.

Multiply both sides by x.

Solve the left side's parentheses.

First multiply 14 and 10: 140.
Then multiply -x and 10: -10x.

Linear equations (one variable) - Example 6

Move 140 to the right side.
And move -3x to the left side.

Then the left side is, +3x - 10x, -7x.
And the right side is -140.

Divide both sides by -7.

Then x = -140/(-7) = 20.