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A merchant wishes to mix gourmet coffee selling for $8 per pound, $10 per pound,
and $15 per pound to get 50 pounds of a mixture that can be sold for $11.70 per pound.
The amount of the $8 coffee must be 3 pounds more than the amount of the $10 coffee.
Find the number of pounds of each that must be used.
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Let x be the pounds of the $10 coffee;
then $8 coffee is (x+3) pounds, and the $15 coffee is the rest (50-x-(x+3)) = (47-2x) pounds.
The combined cost of ingredients and the cost of the mixture is the same,
so we write this equation
10x + 8(x+3) + 15(47-2x) = 50*11.70.
Simplify and find x
10x + 8x + 24 + 15*47 - 30x = 50*11.70
-12x = 50*11.70 - 24 - 15*27
-12x = -144
x = (-144) / (-12) = 12.
ANSWER. 12 pounds of the $10 coffee; 12+3 = 15 pound of the $8 pounds coffee and the rest, 50-12-15 = 23 pounds of the $15 coffee.
CHECK. = 11.70 dollars per pound, the averaged price. ! Precisely correct !
Solved.