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A coffee distributor needs to mix a(n) Kenya coffee blend that normally sells for \$11.60 per pound with a Queen City coffee blend that normally sells for \$14.30 per pound to create 70 pounds of a coffee that can sell for \$13.91 per pound. How many pounds of each kind of coffee should they mix?

A) Write an equation using the information as it is given above that can be solved to answer the question. Use x as your variable to represent the quantity of Kenya coffee blend.
Equation:

11.6x + 14.3(70 - x) = 973.7
11.6x + 1001 - 14.3x = 973.7
- 2.7 x = 973.7 - 1001
-2.7x = -27.3 ---> x = 10 lb of Kenya coffee blend and 60 lb of Queen City coffee blend

3/17/2013

Let's assume that distributor mix "q" lb of Queen City coffee blend in pounds, and "70-q" lb of Kenya coffee blend.
11.6(70-q) + 14.3q = 13.91 × 70
812 - 11.6q + 14.3q = 973.7
812 + 2.7q = 973.7
2.7q = 973.7 - 812
2.7q = 161.7
q = 60 lb of Queen City coffee blend
70 - 60 = 10 lb of Kenya coffee blend
~~~~~~~~~~~~~~~~~~
11.6x + 14.3(70 - x) = 973.7
11.6x + 1001 - 14.3x = 973.7
- 2.7 x = 973.7 - 1001
-2.7x = -27.3 ---> x = 10 lb of Kenya coffee blend and 60 lb of Queen City coffee blend

total pounds of both is 70, so:

x + y = 70

price per pound in the end has to be 13.91, so:

(11.6x + 14.3y)/(x+y) = 13.91

X= QUEEN CITY COFFEE %

1-X = KENYA COFFE %

11.60(1-X) +14.3X =13.91

Opening parenthesis

11.60-11.60X+14.3X=13.91

Subtracting 11.60 both sides of equal sign and rewriting equation.

14.3X-11.6X =13.91-11.60

2.7 X =2.31

DEVIDE BOTH SIDES BY 2.7 TO SOLVE FOR X

X=0.855...5

1-X=.1444445

QUEEN CITY COFFEE% =.85555*100 = 85.56

KENYA COFFEE % =.1444445*100 = 14.44