Percent Change using thePercent Remaining Method

A great method for finding the new amount in one step (and solving other problems).

By Jim Olsen, W.I.U.

If you have a percent increase then the percent remaining is

greater than 100%.

To find the percent remaining just add the percent increase

to 100%

• If the percent increase is 20%, then the percent remaining is 120%.

• If the percent increase is 6.5%, then the percent remaining is 106.5%.

If you have a percent decrease then the percent remaining is

less than 100%.

To find the percent remaining just subtract the percent

decrease from 100%

• If the percent decrease is 20%, then the percent remaining is 80%.

• If the percent decrease is 6.5%, then the percent remaining is 93.5%.

The four key numbers in percent change situations are:

• Original (“old”) amount• New amount• Percent change• Amount of change

Note that I’m not including the percent remaining as one the four key numbers, because it is a direct result of percent change.

Note that usually know (are given) two of these numbers. From any two you can find the other two!

I like to use the template below for the four key numbers in percent change situations

• Original (“old”) amount • New amount• Percent change • Amount of change

The Percent Remaining Method

The key idea is(percent remaining)*(original) = (new)

Example:You start with an amount of $30 and have a 20% increase. Find the new amount (after the increase) and the amount of increase.

------------------------Percent remaining is 120%.

(percent remaining)*(original) = (new)(120%)*($30) = (new)

1.2*$30 = (new)$36 = (new)

The resulting new amount is $36.$36 - $30 = $6. The amount of increase is $6.

Summary (of the previous problem)

$30

20%

Given

ANSWER

$30 $36

20%

$6

?

?

(percent remaining)*(original) = (new)

This can be used, with one step of algebra, to find any of the four numbers (you need to know two of them).

Set-up

$387.09

17.4%

Given

?1999=last year

?1998=previous year

Percent Remaining = 100% + 17.4% = 117.4%

𝑥=original   amount ,  in  1998

(percent remaining)*(original) = (new)

(117.4%)*(__) = $387.09

Solution:

The amount in 1998 for prescription drugs (average per person) was $329.72.

Closing Notes• The percent remaining method works equally well on

percent decrease problems.• Sometimes the percent remaining (written as a decimal,

113% = 1.13) is called the “multiplier.”• The percent remaining method and the multiplier

concept is precisely what’s going on with exponential functions (a topic for another day).

Remember: (percent remaining)*(original) = (new)