Use a Problem-Solving Strategy Quiz
The question sheet
Reveal any answer as you study-
What is the first step in the problem-solving strategy for word problems?
- Solve the equation
- Name what you seek
- Translate into an equation
- Read the problem
Reveal answer
Answer: Read the problem
Source evidence
PDF page 311: Step 1. Read the problem. Make sure all the words and ideas are understood. Step 2. Identify what we are looking for. Step 3. Name what we are looking for. Choose a variable to represent that quantity. Step 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. Step 5. Solve the equation using good algebra techniques. Step 6. Check the answer in the problem and make sure it makes sense. Step 7. Answer the question with a complete sentence.
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According to Step 3, after naming what you look for, you should:
- Read again
- Check the answer
- Choose a variable
- Solve the equation
Reveal answer
Answer: Choose a variable
Source evidence
PDF page 311: Step 1. Read the problem. Make sure all the words and ideas are understood. Step 2. Identify what we are looking for. Step 3. Name what we are looking for. Choose a variable to represent that quantity. Step 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. Step 5. Solve the equation using good algebra techniques. Step 6. Check the answer in the problem and make sure it makes sense. Step 7. Answer the question with a complete sentence.
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In the problem-solving strategy, Step 7 tells you to answer the question by:
- Restating the problem
- Writing a complete sentence
- Choosing a variable
- Multiplying both sides
Reveal answer
Answer: Writing a complete sentence
Source evidence
PDF page 311: Step 1. Read the problem. Make sure all the words and ideas are understood. Step 2. Identify what we are looking for. Step 3. Name what we are looking for. Choose a variable to represent that quantity. Step 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. Step 5. Solve the equation using good algebra techniques. Step 6. Check the answer in the problem and make sure it makes sense. Step 7. Answer the question with a complete sentence.
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In Example 3.1, Pilar bought a purse for $18, one-half the original price. What was the original price?
- $18
- $36
- $9
- $54
Reveal answer
Answer: $36
Source evidence
PDF page 312: The original price of the purse was $36.
PDF page 312: • The answer to the question is: “The original price of the purse was $36.”
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To solve the equation for Pilar's purse, what operation was used on both sides?
- Multiply by 2
- Divide by 2
- Subtract 2
- Add 2
Reveal answer
Answer: Multiply by 2
Source evidence
PDF page 311: Multiply both sides by 2.
PDF page 312: Multiply both sides by 2.
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In Example 3.2, girls were 3 more than twice the boys, with 11 girls. How many boys?
- 4
- 8
- 7
- 11
Reveal answer
Answer: 4
Source evidence
PDF page 313: Simplify. Step 6. Check. First, is our answer reasonable? Yes, having 4 boys in a study group seems OK. The problem says the number of girls was 3 more than twice the number of boys. If there are four boys, does that make eleven girls? Twice 4 boys is 8. Three more than 8 is 11. Step 7. Answer the question. There were 4 boys in the study group.
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What type of word problem does the text say gives a good introduction to the strategy?
- Number problems
- Discount problems
- Percent problems
- Interest problems
Reveal answer
Answer: Number problems
Source evidence
PDF page 313: Now that we have a problem solving strategy, we will use it on several different types of word problems. The first type we will work on is “number problems.” Number problems give some clues about one or more numbers. We use these clues to write an equation. Number problems don’t usually arise on an everyday basis, but they provide a good introduction to practicing the problem solving strategy outlined above.
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In Example 3.3, the difference of a number and six is 13. Find the number.
- 7
- 6
- 13
- 19
Reveal answer
Answer: 19
Source evidence
PDF page 314: Step 6. Check. The difference of 19 and 6 is 13. It checks! Step 7. Answer the question. The number is 19.
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In Example 3.4, the sum of twice a number and seven is 15. Find the number.
- 7
- 8
- 15
- 4
Reveal answer
Answer: 4
Source evidence
PDF page 314: Step 7. Answer the question. The number is 4.
PDF page 314: 2 ⋅ 4 + 7 ≟ 15 15 = 15 ✓
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When a problem asks for two numbers, the text says we should:
- Define both with the same variable
- Use two different variables
- Skip Step 3
- Guess the answer
Reveal answer
Answer: Define both with the same variable
Source evidence
PDF page 314: Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.
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In Example 3.5, one number is five more than another and their sum is 21. The numbers are:
- 8 and 13
- 5 and 16
- 6 and 15
- 10 and 11
Reveal answer
Answer: 8 and 13
Source evidence
PDF page 315: Step 7. Answer the question. The numbers are 8 and 13.
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In Example 3.6, the sum of two numbers is −14 and one is four less than the other. They are:
- −5 and −9
- −6 and −8
- −7 and −7
- −4 and −10
Reveal answer
Answer: −5 and −9
Source evidence
PDF page 316: Step 7. Answer the question. The numbers are −5 and −9.
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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