1. A food factory produces trail mix containing raisins and cashews at a cost of $9 per pound. Every 3-pound container of trail mix contains r pounds of raisins and c pounds of cashews. The factory purchases raisins at $4 per pound and cashews at $8 per pound.
*Choices*
A. 4r+8c=9
B.r+c=3
C.4r+8c=27
D.r+c=9
I choose D, not sure on it though
consider that 3 lbs will cost $27 at $9/lb
so, adding up the value of the raisins and cashews in a 3lb bag,
4r+8c = 27
To solve this problem, let's set up the equation to represent the cost of the trail mix.
The cost of the trail mix per pound is $9, and the total weight of the trail mix is 3 pounds. Since the weight of raisins is represented by r pounds and the weight of cashews is represented by c pounds, the equation can be written as:
(4 * r) + (8 * c) = 9 * 3
Simplifying this equation, we have:
4r + 8c = 27
Therefore, the correct answer is C. 4r + 8c = 27.
To determine the correct choice, let's break down the given information step by step.
1. The factory produces trail mix containing raisins and cashews at a cost of $9 per pound.
This means that for every 1 pound of trail mix, the cost is $9.
2. Every 3-pound container of trail mix contains r pounds of raisins and c pounds of cashews.
This tells us that in each 3-pound container, there are r pounds of raisins and c pounds of cashews.
3. The factory purchases raisins at $4 per pound and cashews at $8 per pound.
This means that the cost of 1 pound of raisins is $4, and the cost of 1 pound of cashews is $8.
Now, let's build the equation based on the given information. Since the cost of each pound of trail mix is $9, and there are 3 pounds in each container, the cost of each container can be calculated as 3 * $9 = $27.
The cost is a result of the sum of the costs of raisins and cashews in the mix. The cost of each pound of raisins is $4, so the cost of r pounds of raisins is 4 * r = 4r. Similarly, the cost of each pound of cashews is $8, so the cost of c pounds of cashews is 8 * c = 8c.
Putting it all together, the equation becomes:
4r + 8c = 27
Now, comparing this equation to the given choices:
A. 4r + 8c = 9 (Incorrect, the cost is $27, not $9)
B. r + c = 3 (Incorrect, this equation does not account for the cost of the ingredients)
C. 4r + 8c = 27 (Correct, this equation matches the one derived from the information)
D. r + c = 9 (Incorrect, this equation does not account for the cost of the ingredients)
Therefore, the correct choice is C. 4r + 8c = 27.