GeekDad Puzzle Of The Week Solution: Fan Club Treasurer

Image by popculturegeek; used under Creative Commons
This weeks puzzle was all about money being spent by 4 groups of fans spending money at a Con. Here it is for old times sake:
We all know how easy it is to spend money in the dealers room at any Con. Well, at a recent Sci-fi Con four groups of fans decided to pool their money and buy awesome stuff for their hangout. Added together the four groups spent $931 total.
There were 25 Trekkies, 20 Star Wars Fans, 18 Bablyon 5 Fans and 12 Farscape Fans
5 Trekkies spent as much as 4 Star Wars Fans
12 Star Wars fans spent as much as 9 Babylon 5 Fans
6 Babylon 5 Fans spent as much as 8 Farscape Fans
This week Eric Ryan with the help of his good friend Reason, and the willing assistance of his passing acquaintance Math (his words not mine) figured out that:
The Trekkies spent $245
The Star Wars Fans spent $245
The Babylon 5 fans spent $294
The Farscape fans spent $147
That answer and the cooperation of a Random Number generator makes Eric this weeks winner of the $50.00 ThinkGeek gift certificate.
Here?s the solution:
T = Total spent by Trekkies
S = Total spent by Star Wars fans
B = Total spent by Babylon 5 fans
F = Total spent by Farscape fans
(1) T + S + B + F = 931
If we let:
t = average amount spent by 1 Trekkie
s = average amount spent by 1 Star Wars fans
b = average amount spent by 1 Babylon 5 fans
f = average amount spent by 1 Farscape fan
From Clue 1 above
T = 25t
S = 20s
B = 18b
F = 12f
(1) becomes
25t + 20s + + 18b + 12f = 931
Now we can use the rearrange the rest of the clues as follows:
(2) 5t = 4s
(2) s = 5/4(t)
(3) 12s = 9b
(3) b = 12/9(s)
From (2)
(3) b = (12/9)(5/4)(t)
(4) 6b = 8f
(4) f= 6/8(b)
From (3)
(4) f = (6/8)(12/9)(5/4)(t)
Now we can drop all that back into the earlier equations:
T = 25t
S = 20(5/4)(t)
B = 18(12/9)(5/4)(t)
F = 12(6/8)(12/9)(5/4)(t)
(1) becomes
25t + 20(5/4)(t) + 18(12/9)(5/4)(t) + 12(6/8)(12/9)(5/4)(t) = 931
95t = 931
t = 9.80
now plug the value of T into the above equations and you get
T = $245
S = $245
B = $294
F = $147
Total = 245 + 245 + 294 + 147 = 931
That was a long road and if your still with me then great! A quick shout out to Rosiland from Girls are Geeks who submitted a correct answer, but alas the random number generating deities did not smile upon her. It was great to see her in the inbox though !
Show up back here on Monday and see what the devious Dave Banks has in store for you. Until then rest your braincells, maybe take them to a spa for a day of pampering.

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