The sum is 109. If four times the smaller number is subtracted from the larger number, the result is 14. Find the two numbers

Question

I am confused and don't understand the steps

Answer 1

There are two numbers.

  Let S = smaller number

        L = larger number

 

Translate:

  "sum is 109"      means     S + L = 109        [eq1]

 

  "four times the smaller number is subtracted from the larger number, the result is 14"       means

          L    -      4S                                                                                 =      14        [eq2]

 

The math (let's use substitution):

    L = 109 - S               [from eq1]

 

  put this into [eq2]:

        (109 - S)     -  4S    =   14

         109 -5S   = 14

             -5S = -95

                S = 19

 

Now, plug that into either equation to find L:

      L = 109 - (19)

     L = 90

 

Check:

   Is    19 + 90 = 109   ?

            109 = 109   ?yes

   Is    90 - 4(19) = 14   ?

          90 - 76 = 14   ?

            14 = 14   ?yes