SOLUTION: I have been working on this one till my head hurts and I made myself more confused than needs to be. A coffee merchant has coffee beans that sell for $9 per pound and $12 per po

Question 86692: I have been working on this one till my head hurts and I made myself more confused than needs to be.
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?
Found 2 solutions by checkley75, ankor@dixie-net.com:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
WHAT YOU NEED IS X POUNDS OF $9 COFFEE ADDED TO (100-X) POUNDS OF $12 COFFEE TO EQUAL 100 POUNDS OF $11.25 COFFEE. SO WE MAKE THE EQUATION THUS:
9X+12(100-X)=100*11.25
9X+1200-12X=1125
-3X=1125-1200
-3X=-75
X=-75/-3
X=25 POUNDS OF $9 COFFEE.
100-25=75 POUNDS OF $12 COFFEE.
PROOF
9*25+12*75=1125
225+900=1125
1125=1125

Answer by ankor@dixie-net.com(12692) (Show Source):
You can put this solution on YOUR website!
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?
:
Here's an easy way to understand it:
Let x = no. of pounds of $12 coffee:
:
The problems states the the resulting amt will be 100 lb, therefore:
(100-x) = no. of pounds of $9 coffee
:
A simple equation:
9(100-x) + 12x = 11.25(100)
:
900 - 9x + 12x = 1125
:
3x = 1125 - 900
:
3x = 225
:
x = 225/3
:
x = 75 lb of $12 coffee, obviously, then we need 25 lb of $9 coffee
:
Check our solution:
9(25) + 12(75) =
225 + 900 = 1125, which is 11.25*100