9.1 Use a problem solving strategy  (Page 5/6)

Consecutive integers are integers that immediately follow each other. Some examples of consecutive integers are:

Notice that each number is one more than the number preceding it. So if we define the first integer as $n,$ the next consecutive integer is $n+1.$ The one after that is one more than $n+1,$ so it is $n+1+1,$ or $n+2.$

The sum of two consecutive integers is $47.$ Find the numbers.

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for.		two consecutive integers
Step 3. Name.		Let n = 1 st integer n + 1 = next consecutive integer
Step 4. Translate. Restate as one sentence. Translate into an equation.
Step 5. Solve the equation.
Combine like terms.
Subtract 1 from each side.
Divide each side by 2.
Substitute to get the second number.
Step 6. Check:
Step 7. Answer the question.		The two consecutive integers are 23 and 24.

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Find three consecutive integers whose sum is $42.$

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for.		three consecutive integers
Step 3. Name.		Let n = 1 st integer n + 1 = 2 nd consecutive integer n + 2 = 3 rd consecutive integer
Step 4. Translate. Restate as one sentence. Translate into an equation.
Step 5. Solve the equation.
Combine like terms.
Subtract 3 from each side.
Divide each side by 3.
Substitute to get the second number.
Step 6. Check:
Step 7. Answer the question.		The three consecutive integers are 13, 14, and 15.

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Key concepts

• Problem Solving Strategy
  1. Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet.
  2. Identify what you are looking for.
  3. Name what you are looking for. Choose a variable to represent that quantity.
  4. Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem. Make sure it makes sense.
  7. Answer the question with a complete sentence.

Practice makes perfect

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.