Math Is Easy - Use Algebra To Solve Word Problem 7!

 

Find four consecutive integers whose sume is -118. (Note 1)

 

Since consecutive integers differ by 1 (1,2,3), we can represent them as follows:

let n represent the smallest of the four consecutive integers; then n + 1 represents the second largest,

n + 2 represents the third largest, and n + 3 represents the largest .

 

We can now create the following equation:

n + (n + 1) + (n + 2) + (n + 3)  = -118

Solve this equation

n + (n + 1) + (n + 2) + (n + 3)  =  -118

n + n + 1 +  n + 2 + n + 3         =  -118  Remove parentheses

 4n + 6                                      =  -118  Add the common terms

 4n + 6                                      =  -118 

      -  6                                      =  -6      Subtract 6 from each side

 4n + 0                                      =  -124

 4n                                            =  -124

 4n/4                                         =  -124/4 Divide each side by 4

  n                                             =   -31

 

Now we substitute the answer for n into the original equation to see if it works.

n + (n + 1) + (n + 2) + (n + 3)  =  -118

-31 + (-31 + 1) + (-31 + 2) (-31 + 3)  = -118

-31  + -30 + -29 + -28 = -118

-118 = -118

 

We must also see if the solution works in the original  problem statement.

Find four consecutive integers whose sume is –118.

Find four consecutive integers (-31, -30, -29, -28  are consecutive integers) whose sume is -118.

Find four consecutive integers (-31  + -30 + -29 + -28 = -118) whose sume is -118.

-118 = -118

 

We have just solved a first degree equation.

 

(Note 1)

The source for the problem statement is:

“Intermediate Algebra  For College Students” by Jerome E. Kaufman

 


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