Page 171 – Percent Problems
Objectives
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Find equivalent fractions, decimals,
and percents.
Solve problems involving percent.
Glossary Terms
Percent – a ratio that compares a number with 100
25% of 40 is 10
percent rate – 25 is the percent rate
the calculated percentage of the base
base (of a percentage) – 40 is the base
number of which a percentage is calculated
Percentage – 10 is the percentage
amount obtained by multiplying a base by a percent rate
Meteorology Application
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Relative humidity is a common example of percent.
At 30ºC, 1 cubic meter of air can hold no more than 26
grams of water.
At this amount, the relative humidity is 100%.
At other amounts, ratios are used to determine the
relative humidity.
If 1 cubic meter of air at 30ºC contains 6.5 g of water, the
relative humidity is 25% because 6.5/26 = ¼ or 25%.
Converting between fractions,
decimals and percents.
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Fractions to decimals – divide the numerator by the
denominator
Decimals to percents – move the decimal point 2 places to
the right
Fractions to percents – change the fraction to a decimal and
the decimal to a percent
Percents to decimals – move the decimal point 2 places to the
left
Decimals to fractions – write the decimal as a fraction and
simplify
Write each percent as a decimal and
as a fraction .
75% =
75
= 0.75
100
75
= 3
100
4
110% = 110 = 1.10
100
1
110 = 11
= 1
10
100
10
4.4% = 4.4 = 44 = 0.044
100
1000
.
44 = 11
250
1000
.
.
The Equation Method
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The equation method is a method for finding an
unknown part of a percent by setting up an equation
25% of 40 is what number (the percentage is unknown)
.25(40) = x
25% of what number is 10 (the base is unknown)
.25x = 10
What percent of 40 is 10 (the percent rate is unknown)
P · 40 = 10 or 40P = 10
The sophomore class is sponsoring a trip to see a play.
Student tickets normally cost $8. If at least 20 people buy
tickets, there is a 30% discount. How much will each
ticket cost at the discounted price.
If there is a 30% discount, that means the discounted price
is 70% of the full price, which is $8.
So, 70% of $8 is what number?
.70(8) = x
5.60 = x
So, the discounted price of the tickets is $5.60.
Examples
What percent of 80 is 15?
Find 115% of 200
P · 80 = 15
What is 115% of 200
80P = 15
x = 1.15(200)
P = 15
x = 230
80
P = .1875
45 is 40% of what number?
18.75%
45 = .4x
45 = x
.4
112.5 = x
A VCR with a sale price of $239.40 is advertised
as 40% off. What was the original price?
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Since the price was 40% off, that means the
$239.40 is 60% of the original price.
So, 239.40 is 60% of what number?
239.40 = .6x
239.40 = x
.6
399 = x
So the original price was $399.
More Applications
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Many types of problems involve finding a
percent of increase or percent of decrease.
It’s important to remember in these types of
problems that the original amount is always
used as the base.
Percent of increase or decrease:
amount of change
= percent of change
original amount
A family is adding additional rooms to their house. The
house originally had 1500 sq ft of floor space. After the
additions, the house will have 1800 sq ft. Find the percent
of increase.
percent of increase =
amount of change
original amount
Amount of change is 1800 – 1500 = 300
original amount is 1500
300
= 0.2 = 20%
1500
.
So the percent of increase in floor space is 20%.
The price of a car that originally sold for $17,000
has been reduced to $14,450. Find the percent of
decrease in the price of the car.
amount of change
percent of decrease =
original amount
Amount of change is 17000 – 14450 = 2550
2550 = 0.15 = 15%
17000
.
So the percent of decrease was 15%.