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A food store makes a 12-lb mixture of granola, clusters, and raisins. The cost of granola is $1.00 per pound, clusters cost $3.00 per pound, and raisins cost $2.00 per pound. The mixture calls for twice as much granola as clusters. The total cost of the mixture is $21.00. How much of each ingredient did the store use?

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Answer:

The food store used  3 lbs of clusters, 6 lbs of granola, and 3 lbs of raisins.

Step-by-step explanation:

Given that:

A food store makes a 12-lb mixture of granola, clusters, and raisins.

The cost of granola = 1.00 per pound

The cost of clusters = 3.00 per pound

The cost of raisins = 2.00 per pound

Let granola be = g; cluster be c and raisins be r

Then, g + c + r = 12

Similarly, the mixture calls for twice as much granola as clusters.

2c + c + r = 12

3c + r = 12

r = 12 - 3c

2c(1) + 3c + 2r = 21

2c + 3c + 2r = 21

5c + 2r = 21

5c + 2(12 -3c) = 21

5c + 24 - 6c = 21

24 - c  = 21

-c = 21 - 24

c = 3

Thus, cluster c = 3 lbs

granola = 2(c) = 2(3) = 6 lbs

raisins = 12 - 3c

= 12 - 3(3)

= 12 - 9

raisins = 3 lbs

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