SOLUTION: Solve each of the following problems. Be sure to show the equations used for the solution. Business and finance. A coffee merchant has coffee beans that sell for $9 per pound and

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Question 74730: Solve each of the following problems. Be sure to show the equations used for the solution.
Business and finance. A coffee merchant has coffee beans that sell for $9 per pound 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?

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of $9.00 beans
Then 100-x=amount of $12.00 beans
Now we know that the value of the $9.00 beans ($9.00)(x) plus the value of the $12.00 beans ($12.00)(100-x) must equal the value of the final mixture (100)($11.25). So our equation to solve is:
$9.00x+$12.00(100-x)=(100)($11.25) get rid of parens
$9.00x+$1200-$12.00x=$1125 subtract $1200 from both sides
$9.00x+$1200-$1200-$12.00x=$1125-$1200 collect like terms
-$3.00x=-$75 divide both sides by -$3.00

x=25 lb of $9.00 beans
100-x=100-25=75 lb of $12.00 beans
CK
25*$9.00+75*$12.00=100($11.25)
225+900=1125
1125=1125

Hope this helps----ptaylor