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Difficulty: MediumWeighted Averages in Applied Contexts

An agricultural enterprise harvests wheat across three distinct parcels of land: Parcel X, Parcel Y, and Parcel Z. Parcel X covers 120120 acres and yields an average of 4545 bushels per acre. Parcel Y covers 8080 acres and yields an average of 6060 bushels per acre. Parcel Z covers 5050 acres and yields an average of 7070 bushels per acre. What is the overall average yield, in bushels per acre, for the entire enterprise across all three parcels?

  1. 54.854.8Answer
  2. B
    58.358.3
  3. C
    61.361.3
  4. D
    45.745.7
  5. E
    61.861.8

Answer

The overall average yield for the entire enterprise is 54.854.8 bushels per acre.
To find the overall average yield across all land, compute total production divided by total acreage. Parcel X yields 5,4005,400 bushels (120×45120 \times 45), Parcel Y yields 4,8004,800 bushels (80×6080 \times 60), and Parcel Z yields 3,5003,500 bushels (50×7050 \times 70). Dividing the combined production of 13,70013,700 bushels by the combined area of 250250 acres gives 54.854.8 bushels per acre.

Step-by-Step Solution

1
Calculate total bushels produced on Parcel X
120 acres×45 bushels/acre=5,400 bushels120 \text{ acres} \times 45 \text{ bushels/acre} = 5,400 \text{ bushels}
Total production for a parcel equals its area multiplied by its yield per acre.
2
Calculate total bushels produced on Parcel Y
80 acres×60 bushels/acre=4,800 bushels80 \text{ acres} \times 60 \text{ bushels/acre} = 4,800 \text{ bushels}
Determine total wheat harvested from Parcel Y.
3
Calculate total bushels produced on Parcel Z
50 acres×70 bushels/acre=3,500 bushels50 \text{ acres} \times 70 \text{ bushels/acre} = 3,500 \text{ bushels}
Determine total wheat harvested from Parcel Z.
4
Sum total bushels and total acreage
Total bushels = 5,400+4,800+3,500=13,700 bushels5,400 + 4,800 + 3,500 = 13,700 \text{ bushels}; Total acres = 120+80+50=250 acres120 + 80 + 50 = 250 \text{ acres}
Weighted average requires total quantity produced divided by total weight (area).
5
Compute the weighted average yield
13,700250=54.8 bushels per acre\frac{13,700}{250} = 54.8 \text{ bushels per acre}
Divide aggregate bushels by aggregate acreage.

Key Concept

Weighted Averages in Applied Contexts
Estimated Time:2m 0s
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Topics

Weighted Averages in Applied Contexts

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