Abel, Bob, Conan, Dave and Elijah divided a certain number of marbles amongst themselves in the following way: Abel took 1 marble and 20% of the remaining marbles, then Bob took 1 marble and 20% of the remaining marbles. Conan, Dave and Elijah did the same. At least how many marbles were there in tbe beginning?

I have two answers but do not know which is correct. Is it a matter of how you interpret the 20% of the remaining ? Math is meant to be black and white but when different ppl say different things ... confusing

3121 and 10

Answer 1

[1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + 5/4 (1 + 5/4 (1 + 5/4 (1 + R))))) units not drawn to scale

[1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + 5/4 (1 + 5/4 (1 + R)))) units not drawn to scale

[1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + 5/4 (1 + R)) units not drawn to scale

[1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + R)

[1][][][][][] --> 1 + R

As R is a multiple of 5, try till you get the first expression as a whole number. Solve using Microsoft Office - Excel, the first whole number is 3121.

There were 3121 marbles in the beginning.

Answer 2

each person has 1 marble plus 20% of the 'remainder'

--> There are 5 marbles + 5x20% of the 'remainder'

--> 100% of the remainder is used / split across the 5 people

So, what is the smallest number that satisfies these conditions

- 100% of the Remainder / 5 is a positive whole number (cannot have a fraction of a marble nor a negative marble)

- the Remainder is greater than zero. If not than, 0/5 = 0 producing a whole number. I don't think they are looking for this answer however. I would think that the Remainder needs to be greater than 0. With this assumption, the Remainder needs to be a multiple of 5.

The smallest multiple of 5 is 5.

--> 5 marbles + 5 marbles = 10 marbles

The smallest number of marbles is 10.