document.write( "Question 80386: 60. Business and finance. A coffee merchant has coffee beans that sell for $9 perpound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture? \n" ); document.write( "
Algebra.Com's Answer #57664 by bucky(2189)\"\" \"About 
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Let N equal the number of pounds of $9 per pound nuts.
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\n" ); document.write( "Let T equal the number of pounds of $12 per pound nuts.
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\n" ); document.write( "From the problem you can infer that when you mix these two amounts together, the total
\n" ); document.write( "weight of the mixture will be 100 lbs. In equation form this becomes:
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\n" ); document.write( "N + T = 100
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\n" ); document.write( "If you multiply $9 times N you get the total dollar amount of N lbs of nuts in the mixture.
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\n" ); document.write( "If you then multiply $12 times T you get the total dollar amount of the T lbs of nuts in
\n" ); document.write( "the mixture.
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\n" ); document.write( "The price of the mixture is given as $11.25 a pound and there are 100 lbs of the mixture.
\n" ); document.write( "So the mixture is worth $11.25 times the 100 lbs of mixture ... a total of $1125.
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\n" ); document.write( "So the dollar amount for each type of nut must add up to be $1125. In equation form this
\n" ); document.write( "is:
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\n" ); document.write( "$9*N + $12*T = $1125.
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\n" ); document.write( "So we have two equations:
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\n" ); document.write( "N + T = 100 and
\n" ); document.write( "9N + 12T = 1125
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\n" ); document.write( "Let's solve these two equations by elimination of the variable N. Multiply all the terms
\n" ); document.write( "in the top equation by 9 so that the term involving N in the top equation equals the term
\n" ); document.write( "that involves N in the bottom equation. The multiplication of the top equation by 9
\n" ); document.write( "results in:
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\n" ); document.write( "9N + 9T = 900
\n" ); document.write( "9N + 12T = 1125
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\n" ); document.write( "Now subtract the bottom equation from the top equation and you get:
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\n" ); document.write( "0*N - 3T = -225
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\n" ); document.write( "and the term 0*N = zero so the equation is just
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\n" ); document.write( " -3T = - 225
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\n" ); document.write( "Solve for T by dividing both sides by -3 to get:
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\n" ); document.write( "(-3T)/(-3) = -225/-3
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\n" ); document.write( "The division leads to:
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\n" ); document.write( "T = 75
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\n" ); document.write( "So the mixture contains 75 lbs of nuts that cost $12 per pound.
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\n" ); document.write( "Since there are 100 lbs of the mixture, and we have accounted for 75 lbs of it, the
\n" ); document.write( "remaining 25 lbs must be the nuts that cost $9 per lb.
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\n" ); document.write( "This is how you do this problem. You could have used other methods to solve the pair of
\n" ); document.write( "equations (methods such as substitution or determinants) but variable elimination
\n" ); document.write( "used above works just as well. Hope this all makes sense to you and you can see how you
\n" ); document.write( "need to find two equations to solve this problem.
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