document.write( "Question 164623This question is from textbook
\n" ); document.write( ": 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.\r
\n" ); document.write( "\n" ); document.write( "What I need to know is what steps were taken to solve this? \n" ); document.write( "
Algebra.Com's Answer #121314 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
you need to solve 3 equations in 3 unknowns.
\n" ); document.write( "4*i + 6*v + 10*x = 114000 (original equation 1)
\n" ); document.write( "8*i + 3*v + 5*x = 72000 (original equation 2)
\n" ); document.write( "2*i + 9*v + 5*x = 81000 (original equation 3)
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\n" ); document.write( "there are several ways to solve.
\n" ); document.write( "one way is as follows:
\n" ); document.write( "multiply first equation by -1
\n" ); document.write( "this will allow you to add up all equations and eliminate the x from the equation.
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\n" ); document.write( "-4*i - 6*v - 10*x = -114000 (equation 1)
\n" ); document.write( "8*i + 3*v + 5*x = 72000 (equation 2)
\n" ); document.write( "2*i + 9*v + 5*x = 81000 (equation 3)
\n" ); document.write( "adding them up gets
\n" ); document.write( "6*i + 6*v = 39000
\n" ); document.write( "dividing both sides by 6 gets
\n" ); document.write( "i + v = 6500
\n" ); document.write( "solve for i gets
\n" ); document.write( "i = 6500 - v
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\n" ); document.write( "take original first and second equation and substitute 6500 - v for i.
\n" ); document.write( "they are reproduced here for easy reference
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\n" ); document.write( "4*i + 6*v + 10*x = 114000 (original equation 1)
\n" ); document.write( "8*i + 3*v + 5*x = 72000 (original equation 2)
\n" ); document.write( "-----
\n" ); document.write( "substituting 6500 - v for i gets
\n" ); document.write( "26000 - 4*v + 6*v + 10*x = 114000 (equation 1)
\n" ); document.write( "52000 - 8*v + 3*v + 5*x = 72000 (equation 2)
\n" ); document.write( "combining like terms gets
\n" ); document.write( "26000 + 2*v + 10*x = 114000 (equation 1)
\n" ); document.write( "52000 - 5*v + 5*x = 72000 (equation 2)
\n" ); document.write( "multiplying equation 2 by 2 gets
\n" ); document.write( "26000 + 2*v + 10*x = 114000 (equation 1)
\n" ); document.write( "114000 - 10*v + 10*x = 144000 (equation 2)
\n" ); document.write( "subtracting equation 2 from equation 1 gets
\n" ); document.write( "-88000 + 12*v = -30000
\n" ); document.write( "adding 88000 to both sides gets
\n" ); document.write( "12*v = 48000
\n" ); document.write( "v = 4000
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\n" ); document.write( "original equations 1 and 2 are reproduced here for easy reference.
\n" ); document.write( "4*i + 6*v + 10*x = 114000 (original equation 1)
\n" ); document.write( "8*i + 3*v + 5*x = 72000 (original equation 2)
\n" ); document.write( "substituting 4000 for v in original equations.
\n" ); document.write( "4*i + 24000 + 10*x = 114000 (equation 1)
\n" ); document.write( "8*i + 12000 + 5*x = 72000 (equation 2)
\n" ); document.write( "multiply equation 2 by 2 gets
\n" ); document.write( "4*i + 24000 + 10*x = 114000 (equation 1)
\n" ); document.write( "16*i + 24000 + 10*x = 144000 (equation 2)
\n" ); document.write( "subtract equation 1 from equation 2 gets
\n" ); document.write( "-12*i = -30000
\n" ); document.write( "-i = -2500
\n" ); document.write( "i = 2500
\n" ); document.write( "you could have used original equations 2 and 3 to solve for i once you knew v.
\n" ); document.write( "you would have gotten the same answer (i = 2500).
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\n" ); document.write( "original equation 3 reproduced here for easy reference
\n" ); document.write( "2*i + 9*v + 5*x = 81000 (original equation 3)
\n" ); document.write( "substituting 2500 for i and 4000 for v in original equation 3 gets
\n" ); document.write( "5000 + 36000 + 5*x = 81000
\n" ); document.write( "combining like terms.
\n" ); document.write( "41000 + 5*x = 81000
\n" ); document.write( "subtracting 41000 from both sides.
\n" ); document.write( "5*x = 40000
\n" ); document.write( "dividing both sides by 5.
\n" ); document.write( "x = 8000
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\n" ); document.write( "answers are:
\n" ); document.write( "i = 2500
\n" ); document.write( "v = 4000
\n" ); document.write( "x = 8000
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\n" ); document.write( "equation 1 reproduced here for easy reference.
\n" ); document.write( "4*i + 6*v + 10*x = 114000 (original equation 1)
\n" ); document.write( "substituting in original equation 1 gets
\n" ); document.write( "4*2500 + 6*4000 + 10*8000 = 114000
\n" ); document.write( "10000 + 24000 + 80000 = 114000
\n" ); document.write( "114000 = 114000
\n" ); document.write( "answer is good.
\n" ); document.write( "works for other equations as well.
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\n" ); document.write( "this is one way to solve it.
\n" ); document.write( "when you get into matrix algebra you'll see other ways to solve it as well.
\n" ); document.write( "i assumed you weren't there yet which is why i chose this solution.\r
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