how to calculate total with unknows?

Question

ann and clara had the same number of stickers. after ann gave clara 48 stickers, clara had 4 times as many stickers. how many stickers do they have together?

Answer 1

"ann and clara had the same number of stickers"    Let this initial number of stickers be x.

 

"ann gave clara 48 stickers"    so, now:

   Ann has (x-48) stickers and Clara has (x+48) stickers

 

"clara had 4 times as many stickers {as Ann}"    means

     (x+48) = 4*(x-48)

 

     x + 48 = 4x - 192      [distribute]

     -3x = -240          [subtract 4x+48 from both sides]

       x = 80     [divide both sides by (-3)]

They each had 80 stickers at the beginning, so they have 160 stockers together.

 

Check:

  Is (80+48) = 4*(80-48)   ?

        128 = 4*32   ?

        128 = 128   ?yes