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

Find four consecutive integers whose sume is -118. (Note1)

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

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

n + 2 represents the third largest, and n + 3 representsthe 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 = -118Remove parentheses

4n + 6 = -118Add 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 answerfor 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 theoriginal 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.

(Note1)

The source for the problem statement is:

Intermediate AlgebraFor College Students by Jerome E. Kaufman


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