Coffee word problem.

Question

The coffee shop charges $8.00 per pound of kenyan french roast and $12.00 per pound for sumatran coffee. How much of each type should be used to make a 24 pound blend that sells for $10.00 per pound?

Answer 1

C: On a 1 pound basis, take alpha pounds of $8/pound coffee and 1 - alpha (making a total of 1pound) pounds of $12 / pound coffee. You want the mixture, 1 pound here, to sell for $10. Therefore 8 (alpha) + 12 (1 -alpha ) = 10 (1). 4 alpha = 2. Alpha = 0.5. You can use this alpha value to apportion any given amount of pounds. Here, you are given total pounds = 24. So you get 24 alpha = 12pounds of $8/pound coffee and 24(1 - alpha) = 24(0.5) = 12 pounds of $12/coffee. Two things to note. If you wanted 1234 pounds of $10/ pound coffee, the apportionment is 617 pounds each (50:50). Why is alpha 0.5? Because, 10, the number you want from the mix, is EXACTLY..........half........way between 8 and 12. Think, think, think. What if one coffee cost was $9, the second was 15, and you wanted the mix to cost $12? Will you get the same alpha?. Guess and then verify. Post a comment. Dr. G. Dr. G.

Answer 2

Let K = pounds of Kenyan-French roast

     S = pounds of Sumatran

 

So 8K + 12S = 10*24 for the total cost.

 

     K + S = 24 for the total weight.

 

 

S = 24 - K, so 8K + 12(24 - K) = 240.

 

8K + 288 - 12K = 240 or 4K = 48 or K = 12.  So, S = 12.

 

We would need 12 pounds each to make a blend that would cost $10 per pound.