Recovering the base ("original") number in percent problems

A% of __ is BTo find A% of __ is B:

Write the equation and Solve.

Use the decimal (or fraction), “of” is multiply, __ is x, “is” is =.

By Jim Olsen, W.I.U.#P12

‘of’ means multiplied by

70% of 800 = (.7)(800) = 560

Change the percent tothe decimal form.

‘of’ becomes ‘times’

Example: Fill in the blank.

20% of __ is 6.

.2 6x

.2 6

.2 .2

x

30x

16

5x

15* 6*5

5x

30x

Example:17.6 is 32% of what number?

17.6 .32x

55 x

17.6 .32

.32 .32

x

Example 1: 18% of the total budget is spent on

transportation. $1368 is spent for transportation. What is the total budget?

Answer: 18% of total budget = transportation

18% of total budget = 1368 .18x = 1368 x= 7600

Total budget is $7,600.

Example 2: Lincoln School raised $6240 in the fund-raiser.

This is 120% of their goal. What was their original goal?

Answer: 120% of goal = amount raised

120% of goal = 6240 1.2x = 6240 x= 5200

Their goal was $5,200.

Example 3: The juice mixture is 50% orange juice. The

mixture has 7 ounces of orange juice. What is the total amount in the mixture?

Answer: 50% of mixture = orange juice

50% of mixture = 7

(½)x = 7 x= 14

The total mixture is 14 ounces.

Closing Notes

Remember

To solve A% of __ is B: Write the equation and Solve. Use the decimal (or fraction), “of” is multiply, __ is x, “is” is =.

#P12