business mathematics percentage formulas. lesson objectives after studying this module, you should...
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![Page 1: Business Mathematics Percentage Formulas. Lesson Objectives After studying this module, you should be able to: identify percentage, rate and base find](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cb05503460f949756a5/html5/thumbnails/1.jpg)
Business MathematicsPercentage Formulas
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Lesson ObjectivesAfter studying this module, you should be able to:
• identify percentage, rate and base
• find the percentage when the rate and the base are given
• find the rate when the percentage and the base are given
• find the base when the percentage and the rate are given
• apply the concept in solving business-related word problems
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Lesson ContentDefinition of Terms
• Rate ( R ) – the rate is the percent
• Base ( B ) – the result obtained when a number is divided by a percent
• Percentage ( P ) – is the product of the rate (in decimal) and the base.
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In symbols,
P = R x B
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How do you identify percentage, rate and base?
Study the statement below:
Forty percent of one hundred fifty is sixty.
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Forty percent of one hundred fifty is sixty.
40% x 150 = 60
40% in decimal is 0.40
Therefore, the above statement written in mathematical symbols is
0.40 x 150 = 60
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Remember
The quantities to the left and right of the word “of” are the rate and the base, respectively. These two are separated from the percentage by the word “is.”
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Example 1Sixty percent of one thousand eighty is what
number?
Now, let’s identify the parts.
R B P
Sixty percent of one thousand eighty is what number?
60% x 1080 =
Percentage (P)
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60% in decimal is 0.60
Therefore, the statement written in mathematical symbols is,
0.60 x 1080 = P 648 = P
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Example 2Twenty percent of three thousand fifty is what
number?
25% x 3,050 =
P
0.25 x 3,050 = P 762.5 = P
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Example 3What number is twenty percent of five hundred
seventy?
P = 20% x 570P = 0.20 x 570
P = 114
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Sometimes, the rate or the base is the one missing. Consider the formula P = R x B, again.
P = R x BTo find rate (R) when P and B are given, divide both sides by
B.
Then,
(Note: R here
is in decimals)
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Example 1 R B PWhat percent of sixty is forty – two?
R x 60 = 42
Since the rate is unknown, use the formula given to solve R.
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Substitute all the given values to the formula.
Change 0.7 to percent, that is, 70%.
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Recall
In changing a decimal number to percent form, simply multiply the given decimal number by 100 and affix percent sign (%).
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Example 2What part of eight hundred ten is one hundred sixty
– two?
R x 810 = 162
(simplify )
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Note!
If asked “what part” in solving the rate, the final answer is express in decimal or fraction form.
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Example 3
Thirty is what percent of eighty?
30 = R x 80
R = 0.375R = 37.5%
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Similarly, to find base (B) when P and R are given, divide both sides of the original formula by R.
That is,
Then,
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Example 1
R B P
Five percent of what number is nine hundred?
5% x B = 900
Since the base is unknown, use the formula given to solve B.
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Substitute all the given values to the formula.
(5% is 0.05 in decimal)
B = 18,000
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Example 2
Eighty percent of what number is three hundred?
80% x B = 300
B = 375
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Example 3
Forty – six is two percent of what number?
46 = 2% x B
B = 2,300
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Note!
It should be noted that the base is usually preceded by the preposition “of”. Sometimes, however, “as great as”, “as many as”, and “as much as” are used instead of “of”.
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Key Concept• To find the percentage when the base and the
rate are known, multiply the base by the rate.
• To find the base when the percentage and the rate are given, divide the percentage by the rate expressed in decimal or in fraction form.
• To find the rate when the percentage and the base are given, divide the percentage by the base.
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AssessmentI. Solve for the value of the unknown.1. Find 12% of 843.
2. Php 42 is 14% of what amount?
3. What is 35% of 80?
4. 6% of 1,080 is what number?
5. 5% of Php1.50 is what part of of Php30.00?
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II. Solve the following problems:6. Bam had 96 pairs of shoes on hand. He
sold 50% of them at P85.00 each, 25% of the remainder at P82.50 each and the rest at P80.00 each. How much did he receive for the entire lot?
7. Charm, a government employee was given an increase in salary of Php 880. If this was a raise of 5% of the salary which she had been receiving, what was her previous monthly salary?
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8. Miranda bought a second-hand laptop for Php12,000 and resold it for Php Php9,000. What part of the resale price was the buying price?
9. After investing 60% of her capital in construction. Engineer Ysabel had Php70,000 left. What was her capital?
10. Xayvion, a financial analyst of a certain firm receives a monthly salary of Php45,000 which is
as much as vice-president’s salary. What is the vp’s salary?