H.) A farmer planted a field of Bt 123 corn and wants to estimate the yield in terms of bushels per acre. He counts 22 ears in 1/1000 of an acre. He determines that each ear has about 700 kernels on average. He also knows that a bushel contains about 90 000 kernels on average. What is the farmer's estimate of yield in bushels/acre?
22 * 700 = 15,400 kernels
90,000 / 15,400 = 5.844 bushels in 1/1000 acre
5.844 * 1,000 = ??? bushels per acre
5,844 bushels per acre
To estimate the farmer's yield in bushels per acre, we need to follow these steps:
Step 1: Calculate the number of ears per acre.
- The farmer counts 22 ears in 1/1000 of an acre.
- Now, we need to scale it up to a full acre.
- There are 43,560 square feet in an acre.
- If the farmer counts 22 ears in 1/1000 of an acre, then we can calculate the number of ears per acre as follows:
Number of ears per acre = (22 ears / 1/1000 acre) * (1 acre / 43,560 square feet)
= (22 * 1000) ears * (1 acre / 43,560 square feet)
≈ 506.9 ears per acre
Therefore, the farmer has approximately 506.9 ears of corn per acre.
Step 2: Calculate the total number of kernels per acre.
- The farmer knows that each ear has about 700 kernels on average.
- So, to find the total number of kernels per acre, we can multiply the number of ears per acre by the average number of kernels per ear:
Total number of kernels per acre = (506.9 ears per acre) * (700 kernels per ear)
= 354,830 kernels per acre
Therefore, the farmer has an estimated total of 354,830 kernels of corn per acre.
Step 3: Calculate the yield in bushels per acre.
- The farmer knows that a bushel contains, on average, about 90,000 kernels.
- To find the yield in bushels per acre, we can divide the total number of kernels per acre by the average number of kernels per bushel:
Yield in bushels per acre = (354,830 kernels per acre) / (90,000 kernels per bushel)
≈ 3.94 bushels per acre
Therefore, the farmer's estimate of the yield in bushels per acre is approximately 3.94 bushels/acre.