Math

Brett and Derrick had 108 marbles altogether. Brett gave away 1/2 as many marbles as what Derrick gave away. The number of marbles Derrick had left was the same as the number of marbles he had given away. If Derrick had 1/2 as many marbles left as Brett, how many marbles did Derrick have at first?

Let   the  number of  marbles  that  Brett had  =  N

Let  the  number  that  Derrick  had  =  108 - N

Let  the  number  that   Derrick gave  away  =  G

Let  the  number  that  Brett gave away  =  (1/2)G

Derrick    had  the  same number left  as  he  gave  away.....this implies that

( 108 -N )  -  G =  G

108 - N  =  2G

N  =  108 - 2G              (1)

And finally  we  have  this  equation

What Brett  had left   = 2* what  Derrick had  left

[N  - (1/2)G ] =   2 G           (2)

Sub (1)  into (2)

[108 - 2G - (1/2)G ]  =  2 G

108  -  (5/2)G  =  2 G

108  =  (9/2)G

108 (2/9)  = G  = 24

Derrick   started with    

2G  =  2(24)  = 48