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