Math Is Easy - Use Algebra To Solve Word Problem 6!

 

Find three consecutive integers whose sume is 42. (Note 1)

 

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

let n represent the smallest of the three consecutive integers; then n + 1 represents the second largest and , n + 2 represents the largest .

 

We can now create the following equation:

n + (n + 1) + ( n + 2)  =  42

Solve this equation

n + (n + 1) + ( n + 2)  =   42

n + n + 1 +  n + 2       =   42  Remove parentheses

 3n + 3                        =   42 Add the common terms

 3n + 3                        =   42 

      -  3                        =   -3           Subtract 3 from each side

 3n + 0                        =   39

 3n                              =   39

 3n/3                           =   39/3 Divide each side by 3

  n                               =   13

 

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

n + (n + 1) + ( n + 2)  =  42

13 + (13 + 1) + (13 + 2) = 42

13 + 14 + 15 = 42

42 = 42

 

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

Find three consecutive integers whose sume is 42.

Find three consecutive integers (13,14,15 are consecutive integers) whose sume is 42.

Find three consecutive integers (13 + 14 + 15 = 42) whose sume is 42.

42 = 42

 

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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