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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:

1. The word "is" means equals in the the equation.
2. The word "of" means times in the equation.
3. 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:

1. 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.
2. 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.
3. 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

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