SOLUTION: A coffee distributor needs to mix a(n) House coffee blend that normally sells for $9.20 per pound with a Rift Valley coffee blend that normally sells for $11.10 per pound to create

Question 1146555: A coffee distributor needs to mix a(n) House coffee blend that normally sells for $9.20 per pound with a Rift Valley coffee blend that normally sells for $11.10 per pound to create 10 pounds of a coffee that can sell for $9.39 per pound. How many pounds of each kind of coffee should they mix?
Answer: they must mix
(Round your answers to the nearest whole number of pounds.)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The standard algebraic solution would be set up like this:

x pounds of House coffee at $9.20 per pound, plus (10-x) pounds of Rift Valley coffee at $11.10 per pound, equals 10 pounds of mixture at $9.39 per pound:

That equation is solved using basic algebra; but it is a bit tedious.

Here is a much faster path to the answer.

(1) 9.39 is 1/10 of the way from 9.20 to 11.10. (9.20 to 9.39 is .19; 9.20 to 11.10 is 1.90. .19/1.90 = 1/10)
(2) Therefore 1/10 of the mixture is the higher priced coffee.

ANSWER: 1/10 of the 10 pounds -- i.e., 1 pound -- is the Rift Valley coffee; the other 9 pounds is the House blend.
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