SOLUTION: Can someone help me on this problem? I need to solve the following problem and show the equation used for the solution: A coffee merchant has coffee beans that sell for $

Algebra ->  Equations -> SOLUTION: Can someone help me on this problem? I need to solve the following problem and show the equation used for the solution: A coffee merchant has coffee beans that sell for $      Log On


   



Question 58286This question is from textbook Beginning Algebra
: Can someone help me on this problem?
I need to solve the following problem and show the equation used for the solution:
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?
Thanks,
Ashley
This question is from textbook Beginning Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount of the $9/pound beans in mixture (in pounds)
Let b = amount of the $12/pound beans in mixture (in pounds)
a + b = 100 (this is given)
Set up this equation:
%289%2Aa+%2B+12%2Ab%29+%2F+100+=+11.25+%2F+1
This simply says "The cost of a pounds of the $9 beans plus
the cost of b pounds of the $12 beans per 100 pound bag must
equal $11.25 per 1 pound."
9a+%2B+12b+=+1125
+a+%2B+b+=+100 (given)
12a+%2B+12b+=+1200 (multiply each side by 12)
Now subtract the 1st equation from the second
3a+=+75
a+=+25 (amt of the %9 beans to use)
b+=+100+-+25
b+=+75 (amt of the $12 beans to use)
check
%289%2Aa+%2B+12%2Ab%29+%2F+100+=+11.25+%2F+1
%289%2A25+%2B+12%2A75%29+%2F+100+=+11.25+%2F+1
do the math- checks OK