This Can Drive You Nuts!
The 3 Wilson brothers and the 2 Martin brothers are sharing a bag of peanuts.
Ash Martin eats one more than a quarter of the whole lot.
Bill Wilson then eats one more than a quarter of the remainder.
Chip Martin eats one more than a quarter of what was left.
And Doug Wilson eats one more than a quarter of the remainder.
At this stage the Martin boys had eaten exactly 100 peanuts more than the Wilson brothers.
Finally, Earl Wilson finishes off all the remaining peanuts that were left.
The 3 Wilson boys ate more peanuts than the 2 Martin brothers, but exactly how many more?
This problem is not an original. It is adapted from a problem posed by Sam Loyd.
The answer is 220.
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2 solutions
yeap , i also got it right
same method..
I was hoping there would be a better metod in the comments...
I gave up cause I thought there was a better method...too...
finally i got it.........
wow! i never thought that i would have to go through all that method and solutions to get the right answer. lol. Well Done!
Got it ryt!!!
This hardly qualifies as a Level 3 problem.
Let S be the number of total peanuts.
A gets 4 1 S + 1 = 4 1 ( S + 4 ) .
B gets 4 1 ( S − 4 1 ( S + 4 ) ) + 1 = 1 6 3 ( S + 4 )
C gets 4 1 ( S − 1 6 3 ( S + 4 ) ) + 1 = 6 4 9 ( S + 4 )
D gets 4 1 ( S − 6 4 9 ( S + 4 ) ) + 1 = 2 5 6 2 7 ( S + 4 )
(See the rule here? n t h person gets 4 n 3 ( n − 1 ) ( S + 4 ) number of peanuts.)
Since A+C=B+D+100,
( S + 4 ) ( 4 1 + 6 4 9 ) = ( S + 4 ) ( 1 6 3 + 2 5 6 2 7 ) + 1 0 0
Which is, 2 5 6 2 5 ( S + 4 ) = 1 0 0
Therefore S = 1020.
Now we know that A=256, B=192, C=144, D=108, and E=320 (E got the remainder)
The difference is (B+D+E)-(A+C), which is 220 peanuts,
Let P be the number of peanuts.
AM (Ash Martin) gets 1+P/4 = (4+P)/4.
Remainder is P - (4+P)/4 = (3P-4)/4
BW (Bill Wilson) gets 1+ 1/4{ (3P-4)/4} = (12+3P)/16
Remainder is (3P-4)/4 - (12 +3P)/16= (9P-28)/16
CM (Chip Martin) gets 1+ 1/4(9P-28)/16= (36+9P)/64
Remainder is (9P-28)/16 - (36+9P)/64= (27P-148)/64
DW (Doug Wilson) gets 1+1/4(27P-148)/64= (27P+108)/256
AM+ CM- BW- DW=100
Solving that you get P= 1020.
AM gets 256
BW gets 192
CM gets 144
DW gets 108
And EW ( Earl Wilson) gets 320.
The 3 Wilson brothers ate 220 peanuts more than the 2 Martin boys