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According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,500. This was $1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?

$5,000

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U.S. Census data shows that the median price of new home in the United States in November 2014 was $280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?

$19,300

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Key concepts

  • Problem-Solving Strategy
    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 algebra 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.
  • Consecutive Integers
    Consecutive integers are integers that immediately follow each other.
    n 1 st integer n + 1 2 nd integer consecutive integer n + 2 3 rd consecutive integer . . . etc.

    Consecutive even integers are even integers that immediately follow one another.
    n 1 st integer n + 2 2 nd integer consecutive integer n + 4 3 rd consecutive integer . . . etc.

    Consecutive odd integers are odd integers that immediately follow one another.
    n 1 st integer n + 2 2 nd integer consecutive integer n + 4 3 rd consecutive integer . . . etc.

Practice makes perfect

Use the Approach Word Problems with a Positive Attitude

In the following exercises, prepare the lists described.

List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.

Answers will vary

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List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.

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Use a Problem-Solving Strategy for Word Problems

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

Two-thirds of the children in the fourth-grade class are girls. If there are 20 girls, what is the total number of children in the class?

30

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Three-fifths of the members of the school choir are women. If there are 24 women, what is the total number of choir members?

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Zachary has 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

125

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One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag?

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There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.

6

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There are 18 Cub Scouts in Pack 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.

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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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