Right before the fifth race at Santa Anita, the word got out that one of the three horses was going to win the race: Lightning Bolt, a 2-1 shot; Golden Honey, a 3-1 shot; or Matchmaker, a 4-1 shot.

Assuming that this tip is true, how much would you have to bet on each of the three horses to be assured of coming out with a $ 39 profit?

Call the bets on the three horses L, G and M from the first letters of the horses' names. Then form equations from each of the possible winning horses:

2L - G - M = 39
-L + 3G - M = 39
-L - G + 4M = 39

solving these simultaneously:

G + 2M = 117
5G - 3M = 117
13G = 585
G = 45
2M = 72
M = 36
2L - 81 = 39
2L = 120
L = 60

giving in summary:

L = 60
G = 45
M = 36

Posted by Charlie on 2013-07-16 17:32:16