SOLUTION: A coffee distributor needs to mix a(n) Mexican Shade Grown coffee blend that normally sells for $10.10 per pound with a Arabian Mocha coffee blend that normally sells for $14.30 pe

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Question 1155346: A coffee distributor needs to mix a(n) Mexican Shade Grown coffee blend that normally sells for $10.10 per pound with a Arabian Mocha coffee blend that normally sells for $14.30 per pound to create 20 pounds of a coffee that can sell for $13.46 per pound. How many pounds of each kind of coffee should they mix?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
v pounds of the 14.30 dollars per pound coffee
M pounds of blend
M-v pounds of the 10.10 dollars per pound coffee
T=13.46 dollars per pound target price of blend
M=20 pounds
L=10.10
H=14.4

L%28M-v%29%2BHv=TM
-
LM-Lv%2BHv=TM
Hv-Lv=TM-LM
v%28H-L%29=M%28T-L%29
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29----------substitute the given values and evaluate.

Evaluate for v, 20%28%2813.46-10.10%29%2F%2814.30-10.10%29%29.

Use v to evaluate 20-v.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Using a traditional algebraic approach....

x pounds at $10.10 per pound, plus (20-x) pounds at $14.30 per pound equals 20 pounds at $13.46 per pound:

10.10%28x%29%2B14.30%2820-x%29+=+13.46%2820%29
10.10x%2B286-14.30x+=+269.2
...

You can finish the problem by that method....

Here is a method for solving this problem by a very different method which requires less time and effort.

Key idea: the ratio in which the two ingredients must be mixed is exactly determined by where the price of the mixture lies between the prices of the two ingredients.

(1) 14.30-10.10 = 4.20
(2) 13.46-10.10 = 3.36
(3) The mixture price of $13.46 per pound is 336/420 = 84/105 = 4/5 of the way from the $10.10 price of the first ingredient and the $14.30 price of the second.
(4) That means 4/5 of the mixture needs to be the second ingredient.

ANSWER: 4/5 of 20 pounds, or 16 pounds, of the Arabian Mocha blend; the remaining 4 pounds of the Mexican blend.

CHECK:
16(14.30)+4(10.10) = 269.2
20(13.46) = 269.2