for two consecutive even integers, three times the smaller plus eight times the larger is 104. find the numbers

Question

consecutive even integers

Answer 1

"two consecutive even integers"  means that we could call them either:

    x  and  (x+2)

 or

   (x-2) and x

 

Let's call them x and (x+2).

 

Translate:

"three times the smaller plus eight times the larger is 104"     means

    3      *             x         +     8       *     (x+2)      =  104

 

The math:

   3x + 8(x+2) = 104

   3x +8x + 16 = 104                [distribute]

     11x = 88                    [collect terms; subtract 16 from both sides]

       x = 8

    x+2 = 10

 

Check:

 8 and 10 are consecutive even integers.

 Does 3*8 + 8*10 = 104   ?

          24 + 80 = 104   ?

             104 = 104?yes