Algebra: Integer task

Question

Find three consecutive integers such that the difference between three times the largest and two times the smallest integer is 30.

Answer 1

"three consecutive integers"

Let them be x, (x+1), and (x+2).

 

"the difference between three times the largest and two times the smallest integer is 30"   means

                                         3 * (x+2)                -         2 * x                               =  30

 

 

The math:

     3(x+2) - 2x = 30

      3x + 6 - 2x = 30                  [distribute]

        x + 6 = 30                      [combine terms]

        x = 24                              [subtract 6 from both sides]

 

The numbers are 24, 25 and 26.

 

Check (very important):

   Is    3*26 -2*24 = 30   ?

            78 - 48 = 30   ?

               30 = 30   ?yes

Answer 2

Hi Joshua, let x represent the smallest number. Then the next number will be x + 1, and the largest number will be x + 2.

 

Equation to solve:

 

3 * (x + 2) - 2 * x = 30

 

3x + 6 - 2x = 30

 

x = 24

 

The three numbers are: 24, 24 + 1, or 25, and 24 + 2, or 26.

 

Questions?