Percent of Base is Amount
𝑃∙𝐵 =𝐴
A pattern to keep in mind:
“10% of $2500 is $250”
Translate to an Equation and Write the Equation, first.
The little word “of” translates to a Multiplication, ∙
The “Base”, 𝐵, comes right after the little word “of”.
The little word “is” translates to an Equal Sign, =
The “Amount”, 𝐴, is the object of the verb “is”.
They’ll tell you two of the values – and the unknown quantity gets represented by a letter.
Solve the Equation
 If the amount 𝐴 is unknown, then Multiply the 𝑃 ∙ 𝐵
 If the base 𝐵 is unknown, then Divide, starting with the 𝐴. Fraction 𝐴/𝑃 or for decimal, 𝐴 ÷ 𝑃
 If the percent 𝑃 is unknown, then Divide, starting with the 𝐴. Convert the fraction or decimal to a percent.
An example of each kind – Amount A unknown, Base B unknown, and Percent P unknown
35% of 220 is what number?
25% of what number is 90?
What percent of 320 is 88?
(or “What number is 35% of 220?”)
(or “90 is 25% of what number?”)
(or “88 is what percent of 320?”)
Think: They tell me that
𝑃 = 35% = 0.35 and 𝐵 = 220.
The Is-Amount 𝐴 is unknown.
Write: 0.35 ∙ 220 = 𝐴
Multiply: Get 𝐴 = 77.
Think: They tell me that
𝑃 = 25% = 0.25 and 𝐴 = 90.
The Of-Base is unknown.
Write: 0.25 ∙ 𝐵 = 90
Divide: 90 ÷ 0.25 is 360
Get 𝐴 = 360.
Answer: 35% of 220 is 77.
Answer: 25% of 360 is 90.
Check by multiplying 0.25(360).
Think: They tell me that
𝐵 = 320 and 𝐴 = 88.
The percent 𝑃 is unknown.
Write: 𝑃 ∙ 320 = 88
Divide: 88 ÷ 320 is 0.275 or 11/40
Multiply by 100 and tack on % sign.
1
Get 𝑃 = 27.5% or 27 %.
2
Answer: 27.5% of 320 is 88.
Check by multiplying 0.275(320).
PercentSolving.docx 10/14/2014 2:36:00 PM -
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- D.R.S.