Ali, Benny and Osman shared a box of marbles. Ali took 1/6 of the marbles, Benny took 2/9 of the marbles and Osman took the remaining marbles. Given that Osman took 64 more marbles than Ali, find the number of marbles in the box at first.

Answer 1

The number of marbles in the box at first is 360.

Ali took 1/6 of the marbles, which is 360/6 = 60 marbles.
Benny took 2/9 of the marbles, which is 360/9 = 40 marbles.
Osman took 64 more marbles than Ali, which is 60 + 64 = 124 marbles.

Therefore, the total number of marbles taken is 60 + 40 + 124 = 224 marbles.

The number of marbles in the box at first is 360 - 224 = 360 marbles.

Answer 2

Several errors in the check of the above solution:
I especially like the last line of
360 - 224 = 360 marbles .....

let the original number of marbles be x
Ali took 1/6 of x or x/6
Benny took 2/9 of x or 2x/9
sofar x/6 + 2x/9 were taken
= 7x/18 were taken, which means that 12x/18 are left
Osman took 12x/18

Osman - Ali = 64
12x/18 - x/6 = 64
12x/18 - 3x/18 = 64
x/2 = 64
x = 128

So there were 128 marbles to start

check:
Ali took 1/6 or 21 1/3 marbles, but we need whole numbers

Ahhhh, the question is flawed