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?

RunningManZZ Apr 20, 2021

#1**+1 **

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

CPhill Apr 20, 2021