+132 Three men are gambling at a bar. They start with money in the ratio 7:6:5 and finish with sums of money in the ratio 6:5:4 (in the same order as before). One of them won $12. How many dollars did he start with?
a) 420 b) 1080 c) 432 d) 120 e) 90
Please show your working and explain( if you can)
I will take a crack at it !!
Let the total amount they started with = m
m / [7+6+5] + 12 = m / [6+5+4]
m =$1,080 - the amount of money they started with as follows:
1,080 / 18 = 60 - average share of each, but we have a ratio of 7:6:5, so:
$420:$360:$300
1,080 / 15 = 72 - the average share of each AFTER the game!!, but we have 6:5:4, and:
72 / 6 = $12 - this is winning of the gambler who started with:
$420 and ended up winning $12, since the ratios are in the same order, so they ended up with:
$12, $10, $8 =$30 in total winning !!!!
Note: Somebody should check these crazy numbers!! But then, I don't gamble!!!!.
I think the above answer is correct, because it just happens that:
The LCM of {7, 6, 5, 4} =420 and the ratio being 7:6:5 or:
$420:$360:$300 =$1,080.
Since $1,080 / [7+6+5] =$60 average per man when they started gambling, and:
Since $1080 / [6+5+4] =$72 average per man if they hadn't lost any money, or:
$432:$360:$288, but one of them ended up with:
$432 - $420 =$12 for the first man, for the ratio of:
$12:$10:$8 =$30 - total wininings for the 3 men, or is it:
$300 - $288 =$12 - Left by the last man, in which case the ratio will be:
$18:$15:$12 =$45 - total winnings for 3 men ????. This last one seems to make more sense, but can't be right because that would mean that he started with $300, which is NOT one of the answers!!!.
+129849 Note that the total amount of money, A, doesn't change.....just the distribution of it does
So....this is a "zero-sum" game....the total amts won + total amts lost = 0
7 : 6 : 5
Means that the first person started with (7/18)A
The second (6/18)A = (1/3)A
The third (5/18)A
In the end ⇒ 6 : 5 : 4
The first person ends up with (6/15)A = ( 2/5)A
The second ends up with (5/15)A = (1/3)A
The last ends up wth (4/15)A
Note that the second person breaks even...he starts with (1/3)A and ends up with the same amount
The first person must have won the $12 because (2/5)A > (7/18)A
And the difference between (2/5A - 7/18A) = 1/90A = $12
So.... $12 is 1/90 of the total amount = $1080
So....the first person must have started with (7/18) * 1080 = $420
And he ends up with (2/5) * 1080 = $432
So.....he makes $12
{Which means that since the second person breaks even....the third person must have lost the $12 }
