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Percents are used to describe parts of
a whole base amount. When one of the parts of the relationship is
unknown, we can solve an algebraic equation for the unknown quantity.
(The solution methods shown on this page are of an algebraic,
sentence translation nature.
Of course, other methods of solution are also possible.)
There are two
main types of problems dealing with percents:
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1.
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In the
first type of problem, the percent
is given.
In these problems, you will change the percent to a
decimal.
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To
change a percent to a decimal, divide the number by 100.
This will move the decimal point two places to the left.
| Example: |
Find
7% of 250.
(This can also be read "What number is 7% of 250?")
Let x = the
answer
x = 7% • 250
x = 0.07 • 250
changing 7% to a decimal
x = 17.5
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Remember that
the word "of " means
to multiply! |
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| Example: |
30 is
15% of what number?
Let n = the
answer ("what number")
30 = 15% • n
30 = 0.15 • n
changing 15% to a decimal
30/0.15 = n
dividing both sides by 0.15
200
= n
n = 200 |
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Remember that
the word "of " means
to multiply! |
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2.
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In
the
second type of problem, you are looking
for the percent.
In these problems, you will represent the % as a fraction.
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| Example: |
3
is what percent of 12?
Let x% =
the
percent.
Writing
this problem literally we would get:
The
answer is 25%.
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To
change a percent to a fraction, divide the percent value by 100. |
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Example:
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If 120
million roses were sold on Valentine's Day, and 75% of the roses
were red, how many red roses were sold on Valentine's Day?
Let x = the
number of red roses sold
x = 75% of 120
x = 0.75 • 120
x = 90 million red roses sold
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Example:
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Juan missed
6 out of 92 questions on a test. To the nearest percent, what
percent of the questions did he solve correctly?
If he missed 6
questions, he got 86 questions correct. Re-word the question
to be "86 is what percent of 92"?
To the nearest percent, he got 93% correct.
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