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?
My problem is that I can't figure out the correct way to set this up.
This is how I am setting the problem up...then I am stuck.
900x+1200y=1125
-900(900x+1200)y=(-900)(1125)
-1,080,000y=-1,012,500
y=.9375
The final product will be 100 lbs selling for $1125. So 1125 = 9x + 12 (100-x). Where x is the number of pounds of the cheaper brand. You will then need (100 - x) pounds of the other brand to fill the mixture b/c x + (100-x) = 100. So solving 1125 = 9x + 12(100-x) leaves you with x = 25. So y (or 100-x) is 75.
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