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Answer :
1.Flow in Ducts: 1,600 cu ft/min in the first duct, 1,200 cu ft/min in the second duct. So the correct option is e.
2.Mixing Butterfat Cream and Milk: 79 lb of 40%-butterfat cream, 158 lb of 1%-butterfat milk. So the correct option is d.
1. Flow in Ducts:
Let x be the flow in the first duct.
Then, the flow in the second duct would be x + 400 cubic feet per minute.
The total flow is 2,800 cubic feet per minute, so we can write the equation:
x + (x + 400) = 2800
Solving for x:
2x + 400 = 2800
2x = 2400
x = 1200
The flow in the first duct (x) is 1200 cubic feet per minute.
The flow in the second duct (x + 400) is 1600 cubic feet per minute.
Therefore, the correct answer is: e. The flow is 1,600 cu ft/min in the first duct, the flow is 1,200 cu ft/min in the second duct.
2. Mixing Butterfat Cream and Milk:
Let x be the pounds of 40%-butterfat cream to mix.
Then, the pounds of 1%-butterfat milk to mix would be (237 - x) since the total amount is 237 lb.
The equation can be set up based on the butterfat content:
0.4x + 0.01(237 - x) = 0.14(237)
Solving for x:
0.4x + 2.37 - 0.01x = 33.18
0.39x = 30.81
x = 79
So, the dairyman needs to mix 79 pounds of 40%-butterfat cream and (237 - 79) = 158 pounds of 1%-butterfat milk.
Therefore, the correct answer is: d. 79 lb of 40%-butterfat cream, 158 lb of 1%-butterfat milk.
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