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Question 39134: The Marble Club has six members. Each member contributes his marbles and holds office on the basis of the number of marbles he contributes. The president has contributed 104 marbles more than the vice-president, who in turn has contributed 203 more than the treasurer. The secretary donated 1/2 the amount of the vice-president. The marble counter contributed 3 more than the sergeant at arms, and they have contributed 485 marbles together. If the total number of marbles is 3,886, how many did each contribute?
(not from a text) Please help me solve, Thank you
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Okay, this will take a while but here goes...
Let the variables be P, V, T, S, M, and G, for prez, vice-prez, treas, sec, marb, and sergeant.
From the problem we have
P = V + 104
V = T + 203 or T = V - 203
S = (1/2)V
M = G + 3
M + G = 485
Main equation: P + V + T + S + M + G = 3886
Let's do M and G first.
By substitutng, we get
2G + 3 = 485
2G = 482
G = 241
M = 244
Now plug everything into the main equation and we get
(V+104) + V + (V-203) + (1/2)V + 485 = 3886
combining we get
(7/2)V + 386 = 3886
(7/2)V = 3500
V = 1000
so then
P = 1104
S = 500
T = 797
and we're done! Whew!
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