Finding Integers

Question

For 2 consecutive intgers, the result of adding the smaller integer and triple the larger integer is 79. What are the two integers.

Answer 1

Let the two "Consecutive integers" be x and (x+1).

 

  "adding the smaller integer and triple the larger integer is 79"    means

                           x              +      3   ( x+1)                =    79

 

x + 3(x+1) = 79

 4x + 3 = 79          [distribute; collect terms]

  4x = 76              [subtract 3 from both sides]

   x = 19               [divide both sides by 4]

 

The consecutive integers are 19 and 20.

 

Check:

  Is   19 + 3(20) = 79   ?

         19 + 60 = 79  ?

            89 = 79   ?yes

Answer 2

Revised solution below, after correcting an error:

 

Let the two consecutive integers be n and n + 1, with n + 1 the greater number.

 

n + 3(n + 1) = 79

 

4n + 3 = 79

 

4n = 76

 

n = 76/4 = 19

 

n + 1 = 19 + 1 = 20

 

The two integers are 19 and 20.  

 

Test:  19 + 3(20) = 19 + 60 = 79 [good]