Question 164623This question is from textbook
: Business: On monday, a computer manufacturing company sent out three shipments. The first order; which contained a bill for $114,000, was for four model I, six model V, and 10 model X computers. The second shipment, which contained a bill for $72000, was for eight Model I, three model V, and five model X computers. The third shipment, which contained a bill for $81000, was for two model I, nine model V and five model X computers. What does the manufacturers charge for each model V computer.
What I need to know is what steps were taken to solve this?
This question is from textbook
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! you need to solve 3 equations in 3 unknowns.
4*i + 6*v + 10*x = 114000 (original equation 1)
8*i + 3*v + 5*x = 72000 (original equation 2)
2*i + 9*v + 5*x = 81000 (original equation 3)
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there are several ways to solve.
one way is as follows:
multiply first equation by -1
this will allow you to add up all equations and eliminate the x from the equation.
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-4*i - 6*v - 10*x = -114000 (equation 1)
8*i + 3*v + 5*x = 72000 (equation 2)
2*i + 9*v + 5*x = 81000 (equation 3)
adding them up gets
6*i + 6*v = 39000
dividing both sides by 6 gets
i + v = 6500
solve for i gets
i = 6500 - v
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take original first and second equation and substitute 6500 - v for i.
they are reproduced here for easy reference
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4*i + 6*v + 10*x = 114000 (original equation 1)
8*i + 3*v + 5*x = 72000 (original equation 2)
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substituting 6500 - v for i gets
26000 - 4*v + 6*v + 10*x = 114000 (equation 1)
52000 - 8*v + 3*v + 5*x = 72000 (equation 2)
combining like terms gets
26000 + 2*v + 10*x = 114000 (equation 1)
52000 - 5*v + 5*x = 72000 (equation 2)
multiplying equation 2 by 2 gets
26000 + 2*v + 10*x = 114000 (equation 1)
114000 - 10*v + 10*x = 144000 (equation 2)
subtracting equation 2 from equation 1 gets
-88000 + 12*v = -30000
adding 88000 to both sides gets
12*v = 48000
v = 4000
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original equations 1 and 2 are reproduced here for easy reference.
4*i + 6*v + 10*x = 114000 (original equation 1)
8*i + 3*v + 5*x = 72000 (original equation 2)
substituting 4000 for v in original equations.
4*i + 24000 + 10*x = 114000 (equation 1)
8*i + 12000 + 5*x = 72000 (equation 2)
multiply equation 2 by 2 gets
4*i + 24000 + 10*x = 114000 (equation 1)
16*i + 24000 + 10*x = 144000 (equation 2)
subtract equation 1 from equation 2 gets
-12*i = -30000
-i = -2500
i = 2500
you could have used original equations 2 and 3 to solve for i once you knew v.
you would have gotten the same answer (i = 2500).
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original equation 3 reproduced here for easy reference
2*i + 9*v + 5*x = 81000 (original equation 3)
substituting 2500 for i and 4000 for v in original equation 3 gets
5000 + 36000 + 5*x = 81000
combining like terms.
41000 + 5*x = 81000
subtracting 41000 from both sides.
5*x = 40000
dividing both sides by 5.
x = 8000
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answers are:
i = 2500
v = 4000
x = 8000
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equation 1 reproduced here for easy reference.
4*i + 6*v + 10*x = 114000 (original equation 1)
substituting in original equation 1 gets
4*2500 + 6*4000 + 10*8000 = 114000
10000 + 24000 + 80000 = 114000
114000 = 114000
answer is good.
works for other equations as well.
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this is one way to solve it.
when you get into matrix algebra you'll see other ways to solve it as well.
i assumed you weren't there yet which is why i chose this solution.
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