A local grocery store makes a 9-pounds 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?

The quantity of each ingredient used:

2 pounds of sunflower, 4 pounds of raisins and 3 pounds of chocolate-covered peanuts.

Step-by-step explanation:

From the question, the total weight of the mixture is 9 pounds.

Also, the mixture calls for twice as many raisins as sunflower seeds, (that is for every 1 pound of sunflower, we have 2 pounds of raisins)

Let the weight of the sunflower seeds be s pounds

Then, the weight of the raisin will be 2s pounds

The weight of chocolate-covered peanuts will be the sum of the weights of the raisin and sunflower seeds deducted from 9 pounds, that is

9 - (2s + s) = 9 - 3s pounds

Hence, the mixture contains 9-3s chocolate-covered peanuts.

Now, from the question, the raisins cost $2 per pound, the  sunflower seeds cost $1 per pound, and the chocolate-covered peanuts cost $1.50 per per pounds; and the total cost of the mixture is $14.50. Then, we can write that

$2(2s) + $1(s) + $1.5(9-3s) = $14.50

$4s + $1s + $13.5 -$4.5s = $14.50

$0.5s = $14.50 - $ 13.50

$0.5s= $1.00

s = $1.00 / $0.5

s = 2

Hence, the weight of sunflower used is 2 pounds

The weight of raisin used is 2s = 2*2 pounds = 4 pounds

and the weight of chocolate-covered peanuts is 9 - 3x = 9 - 3*2 pounds

= 9 - 6 pounds = 3 pounds

Hence, the quantity of each ingredient used:

2 pounds of sunflower, 4 pounds of raisins and 3 pounds of chocolate-covered peanuts.

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