Question 1094980: a local grocery store store makes a 9-pound mixture of trail mix. the trail mix contains raisins,sunflower seeds,and chocolate covered peanuts. the raisins cost $2 per pound, the sunflower seeds cost $1 per pound, and the chocolate covered peanuts cost $1.50 per pound. the mixture calls for twice as many raisins as sunflower seeds. the total cost of the mixture is $14.50. how much of each ingredient did the store use
Answer by ikleyn(52879)   (Show Source):
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A local grocery store makes a 9-pound mixture of trail mix. The trail mix contains raisins, sunflower seeds, and chocolate
covered peanuts. The raisins cost $2 per pound, the sunflower seeds cost $1 per pound, and the chocolate covered peanuts cost $1.50
per pound. the mixture calls for twice as many raisins as sunflower seeds. the total cost of the mixture is $14.50.
How much of each ingredient did the store use
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Let x = weight of sunflower seeds (in pounds).
Then the weight of the raisins is 2x pounds and the weight of the chocolate covered peanuts is 9 - x - 2x = 9-3x pounds.
The "cost equation" is
2*(2x) + 1*x + 1.50*(9-3x) = 14.50 dollars.
=============> 4x + x + 13.5 - 4.5x = 14.5 ====> 0.5x = 14.5 - 13.5 = 1 ===> x = 2.
Answer. 2 pounds of sunflower seeds, 4 pound of raisins and 9-3*2 = 3 pounds of the chocolate covered peanuts.
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