How do I set up the equation for this word problem? A takes 1/2 of the diamonds plus 1 from the table. B takes 2/3 of what remai
ns. C takes 2/3 of what remains plus 1. One diamond is left. How many diamonds had originally been on the table? Answer is 38 but I don't know how to set it up.
The first thief takes (1/2 x + 1) . What remains ? x - (1/2x + 1)
So the 2nd thief takes 2/3 of [ x - (1/2x + 1) ]
What remains ? x - 2/3 [ x - (1/2x + 1) ]
So the 3rd thief takes 2/3 of { x - 2/3 [ x - (1/2x + 1) ] } and he takes 1 more .
What remains ? x - ( 2/3 { x - 2/3 [ x - (1/2x + 1) ] } + 1 )
And that whole ugly thing is equal to ' 1 ', so you can solve it for 'x'..
The whole problem from here on is an exercise in simplifying an expression with a bunch of 'nested' parentheses in it. =============================================== This is a lot harder than just solving the problem with logic and waving your hands in the air. Here's how you would do that:
Start from the end and work backwards:
-- One diamond is left. -- Before the 3rd thief took 1 more, there were 2. -- That was 1/3 of what was there before the 3rd man took 2/3. So he found 6 when he arrived. -- 6 was 1/3 of what was there before the second thief helped himself. So there were 18 when the 2nd man arrived. -- 18 was 1 less than what was there before the first thief took 1 extra. So he took his 1 extra from 19. -- 19 was the remaining after the first man took 1/2 of all on the table. So there were 38 on the table when he arrived.
