FORMULABANK

Finding the Whole from a Percentage

Example: 13% of a number is 260. What is the whole number?

$\frac{260}{13\%}=\frac{260}{0.13}=2000$

Finding the Original Number After a Percentage is Added
 

Finding the Original Number When the Number After a Percentage Increase is Known

General Formula:

$\frac{\mathrm{number\; after\; increase}}{100\%+\mathrm{increase\; percentage}}=\mathrm{original\; number}$

Example:
A number has increased by 20% to 150. What was the original number?

This means the original number is 100%, and 20% is added to it, resulting in 150.

$\frac{150}{100\%+20\%}=125$

Method Using CAS:

$x+x·20\%=150$

Solved using the CAS tool WordMat:

$x=125$