The sum of two numbers a and b is 28 while the difference between them is equal to 8 if a is larger than b what are these two numbers

Question

I can’t find the difference between 8

 

Answer 1

"a is larger than b"   means

    Let a= larger number

          b = smaller number

"The sum of two numbers a and b is 28"     means         a + b = 28

"The difference between them is equal to 8    means      a  - b =   8        [note: a is larger]

                           (elimination; add equations)     -----------------------

                                                                                2a     =  36

     a = 18    [divide both sides by 2]

 

    a  +  b  =  28

    a  -  b  =     8

 -----------------------     [elimination; subtract equations]

         2b  =  20

           b = 10

 

Note: You could also use substitution.

 

Check:

    Is  18 + 10 = 28   ?

            28 = 28   ?yes

   Is  18 - 10 = 8

              8 = 8   ?yes