<< Chapter < Page  Chapter >> Page > 
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:
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.
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 $\mathrm{31}.$ Find the numbers.
−15, −16
Find three consecutive integers whose sum is $42.$
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 $\mathrm{36}.$
−11, −12, −13
Use a Problemsolving Strategy for Word Problems
In the following exercises, use the problemsolving strategy for word problems to solve. Answer in complete sentences.
Twothirds of the children in the fourthgrade 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.
Notification Switch
Would you like to follow the 'Prealgebra' conversation and receive update notifications?