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2003
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370
Using Equations to Solve Percent Problems 









How
to set up simple linear equations to solve percent problems 
calculator,
paper and pencil 
Not
all folks like to use proportions for solving percent problems,
and indeed there is another method. You can set up simple
linear equations for many percent problems if you remember
three little things:
 The
word "is" means equals in the the equation.
 The
word "of" means times in the equation.
 The
thing you are trying to find is the variable.
*NOTE:
if it's the percent you are trying to find, the equation
will generate a number that is equivalent to the percent.
You will have to change it back into a percent by moving
its decimal two spots right and adding a % sign. See
example 3 below.
Let's
look at a few:
 What is 35
percent of 80?
x
= .35(80)

We
put the variable first because the sentence starts
with the word, "what." Next comes the
equal sign because of the word, "is."
35 percent is written as a decimal because you must
always convert
percents to decimals or fractions before you
can use them in equations. Finally, we multiply
by 80 because of the word, "of."
The
answer to this one is 28.

 16% of what
number is 2?
0.16x
= 2

Remember,
"of" means times, "is" means
equals, and the thing you don't know is your variable.
Also, remember you must change the percent to a
usable number before you can work the equation.
Dividing
both sides of this equation by 0.16, gives an
answer of 12.5.

 What percent
of 350 is 70?
x(350)
= 70

Most
math texts and teachers will write this equation
as, 350x = 70,
because it is traditional to put the number being
multiplied in front of the variable. This
is called the "numerical coefficient"
of the variable.
Dividing
both sides of this equation by 350 gives us 70/350
which is 0.2.
*Remember
this must be converted back into a PERCENT because
the problem asked for "What percent."
So the final answer is achieved by moving the decimal
2 spots to the right and affixing the percent sign,
20%.


 43%
of 32 is what number? (answer)
 What
% of 300 is 78? (answer)
 15 is 60%
of what number? (answer)

 Go
ahead and try The
Customizable Percent Test
(You
can insert your own names to create funny percent problems,
solve them and get a password to a funky treasure room.)



340 The
History of Percent
350
Converting Percents
to Decimals and Fractions
360 Solving
Percents Using Proportions
The
Customizable Percent Test
