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By the end of this section, you will be able to:
  • Translate and solve basic percent equations
  • Solve percent applications
  • Find percent increase and percent decrease
  • Solve simple interest applications
  • Solve applications with discount or mark-up

Before you get started, take this readiness quiz.

  1. Convert 4.5% to a decimal.
    If you missed this problem, review [link] .
  2. Convert 0.6 to a percent.
    If you missed this problem, review [link] .
  3. Round 0.875 to the nearest hundredth.
    If you missed this problem, review [link] .
  4. Multiply (4.5)(2.38).
    If you missed this problem, review [link] .
  5. Solve 3.5 = 0.7 n .
    If you missed this problem, review [link] .
  6. Subtract 50 37.45 .
    If you missed this problem, review [link] .

Translate and solve basic percent equations

We will solve percent equations using the methods we used to solve equations with fractions or decimals. Without the tools of algebra, the best method available to solve percent problems was by setting them up as proportions. Now as an algebra student, you can just translate English sentences into algebraic equations and then solve the equations.

We can use any letter you like as a variable, but it is a good idea to choose a letter that will remind us of what you are looking for. We must be sure to change the given percent to a decimal when we put it in the equation.

Translate and solve: What number is 35% of 90?

Solution

.
Translate into algebra. Let n = the number. .
Remember "of" means multiply, "is" means equals.
Multiply. .
31.5 is 35% of 90
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Translate and solve:

What number is 45% of 80?

36

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Translate and solve:

What number is 55% of 60?

33

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We must be very careful when we translate the words in the next example. The unknown quantity will not be isolated at first, like it was in [link] . We will again use direct translation to write the equation.

Translate and solve: 6.5% of what number is $1.17?

Solution

.
Translate. Let n = the number. .
Multiply. .
Divide both sides by 0.065 and simplify. .
6.5% of $18 is $1.17
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Translate and solve:

7.5% of what number is $1.95?

$26

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Translate and solve:

8.5% of what number is $3.06?

$36

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In the next example, we are looking for the percent.

Translate and solve: 144 is what percent of 96?

Solution

.
Translate into algebra. Let p = the percent. .
Multiply. .
Divide by 96 and simplify. .
Convert to percent. .
144 is 150% of 96

Note that we are asked to find percent, so we must have our final result in percent form.

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Translate and solve:

110 is what percent of 88?

125%

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Translate and solve:

126 is what percent of 72?

175%

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Solve applications of percent

Many applications of percent    —such as tips, sales tax, discounts, and interest—occur in our daily lives. To solve these applications we’ll translate to a basic percent equation, just like those we solved in previous examples. Once we translate the sentence into a percent equation, we know how to solve it.

We will restate the problem solving strategy we used earlier for easy reference.

Use a problem-solving strategy to solve an application.

  1. Read the problem. Make sure all the words and ideas are understood.
  2. Identify what we are looking for.
  3. Name what we are looking for. Choose a variable to represent that quantity.
  4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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