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

 Page 5 / 6

One number is eight more than twice another. Their sum is negative four. Find the numbers.

−4, 0

One number is three more than three times another. Their sum is negative five. Find the numbers.

−2, −3

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

$\begin{array}{c}\phantom{\rule{0.2}{0ex}}\\ \phantom{\rule{0.2}{0ex}}\\ \phantom{\rule{0.2}{0ex}}\\ \phantom{\rule{0.2}{0ex}}\\ \hfill \text{...}1,2,3,4\text{,...}\hfill \end{array}$
$\text{...}-10,-9,-8,-7\text{,...}$
$\text{...}150,151,152,153\text{,...}$

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 $n+2.$

$\begin{array}{cccc}n\hfill & & & \text{1st integer}\hfill \\ n+1\hfill & & & \text{2nd consecutive integer}\hfill \\ n+2\hfill & & & \text{3rd consecutive integer}\hfill \end{array}$

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.

The sum of two consecutive integers is $95.$ Find the numbers.

47, 48

The sum of two consecutive integers is $-31.$ Find the numbers.

−15, −16

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.

Find three consecutive integers whose sum is $96.$

31, 32, 33

Find three consecutive integers whose sum is $-36.$

−11, −12, −13

## 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.

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?

There are 30 children in the class.

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or in general
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in general
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On having this app for quite a bit time, Haven't realised there's a chat room in it.
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Good
Berger describes sociologists as concerned with
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