a captain has three companies, one of swiss, another of swabians, and a third of saxons. he wishes to storm with part of these troops, and he promises a reward of 901 crowns, on the following condition; namesly, that each soldier of the company, which assaults, shall receive 1 crown, and that the rest of the money shall be equally distributed among the two other companies. now, it is found, that if the swiss make the assault, each soldier of the other companies will receive half-a-crown; that if the swabians assault, each of the others will receive 1/3 of a crown; and, lastly, if the saxons make the assault, each of the others will receive 1/4 of a crown.
required the number of men in each company??
thanks so much if you can help!
2007-03-24 18:03:22 · 6 answers · asked by jimmy 1 in Science & Mathematics ➔ Mathematics
Hmm.. whoever set you this must be so mean.. I can't get it sorry
2007-03-24 18:11:48 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Just a linear system of 3 eqns in 3 variables...
Let a = number of Swiss, b = number of Swabians, c = number of Saxons.
Then if the Swiss assault:
a*1 + (b+c)*1/2 = 901
Similarly:
b*1 + (a+c)*1/3 = 901
c*1 + (a+b)*1/4 = 901
a + (b+c)/2 = 901
b + (a+c)/3 = 901
c + (a+b)/4 = 901
2a + b +c = 1902 [1]
a + 3b + c = 2703 [2]
a + b + 4c = 3604 [3]
You can solve either by back-substitution or Gauss-Jordan elimination. Let's do back-substitution:
[2] => c = 3(901) - a - 3b
[3] => b = 4(901) -a -4c
=> b = 4(901) -a -4(3(901) - a - 3b)
b = 4(901) -a -12(901) + 4a + 12b
b = 3a + 12b -8(901)
8(901) -3a = 11b
b = (8(901) -3a)/11
Finally back-substituting in [1]...
2a + b + 3(901) - a - 3b = 1902
a -2b = -901
a - 2(8(901) -3a)/11 = -901
11a - 16(901) +6a = -11(901)
17a = 5(901)
a = 5*53 = 265
b = (8(901) -3a)/11
b = 583
c = 3(901) - a - 3b
c = 2703 - 265 - 3(583)
c = 689
ANSWER: a=265, b=583, c=689
2007-03-25 01:07:11 · answer #2 · answered by smci 7 · 2⤊ 0⤋
You need to solve the following system of equations:
a+ (b+c)*1/2 = 901
b+ (a+c)*1/3 = 901
c + (a+b)*1/4 = 901
where a=swiss, b=swabs, c=saxons
This turns out to be a=265, b=583, and c=689
2007-03-25 01:15:18 · answer #3 · answered by jnamnath 1 · 1⤊ 0⤋
good luck with an answer 4 this, but swiss has more pple than swa then sax. if u want a real answer email euphoman09@aol.com, he is a true genius and will help u.
2007-03-25 01:20:06 · answer #4 · answered by wheels 2 · 0⤊ 1⤋
you need to know how amny men are in each company
2007-03-25 01:12:29 · answer #5 · answered by Tiger 3 · 0⤊ 1⤋
The answer is zero....they're all women.
2007-03-25 01:12:57 · answer #6 · answered by Michael E 5 · 0⤊ 1⤋