Find two numbers given that their sum is 48 and the smaller number is equal to one-fifth of the larger number

Question

Answer will come by subsitution or elimination method

Answer 1

Let x = smaller number

     y = larger number

 

"their sum is 48"     means     x + y = 48    [eq1]

"smaller number is equal to one-fifth of the larger number"   means    x = (1/5)y    [eq2]

 

Elimination method:

   x  +   y   = 48       [eq1]

  5x  -   y  =    0       [from eq2]  

--------------------     [elimination; add equations]

  6x          =  48

  x            =   8

  x    +  y  =  48       [eq1]

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

         - y  =  - 40

           y  =  40         [divide by (-1)]

 

Check:

    Is   8 + 40 = 48   ?

              48 = 48   ?yes

    Is   8 = (1/5)40   ?

          8 = 8   ?yes

Answer 2

x + x/5 = 48

 

6x/5 = 48

 

6x = 240

 

x = 40

x/5 = 8