Question

which of the following is closest to the total weight, in pounds, of the pumpkins the farmer harvested?
a farmer harvested a total of 364 pumpkins. the pumpkins had an average weight of 10.9 pounds.
which of the following is closest to the total weight, in pounds, of the pumpkins the farmer harvested?

○ 3,000
○ 3,300
○ 4,000
○ 4,400

Explanation:

Step1: Recall the formula for total weight

The formula for total weight when average weight is known is \( \text{Total Weight} = \text{Number of Items} \times \text{Average Weight} \). Here, the number of pumpkins is 364 and the average weight is 10.9 pounds. So we need to calculate \( 364 \times 10.9 \).

Step2: Estimate the product

To estimate, we can round 364 to 360 and 10.9 to 11 (or we can do a rough multiplication). Let's do \( 364 \times 10.9 \approx 364 \times 11 - 364 \times 0.1 \). First, \( 364 \times 11 = 364\times(10 + 1)=3640+364 = 4004 \). Then, \( 364 \times 0.1 = 36.4 \). So \( 4004 - 36.4 = 3967.6 \). Alternatively, we can round 364 to 360 and 10.9 to 11: \( 360\times11 = 3960 \). Both estimates are close to 4000? Wait, wait, maybe I made a mistake. Wait, 364 times 10.9: let's calculate it more accurately. \( 364 \times 10 = 3640 \), \( 364 \times 0.9 = 327.6 \). Then add them: \( 3640 + 327.6 = 3967.6 \). Now let's check the options: 3000, 3300, 4000, 4400. 3967.6 is closest to 4000? Wait, no, wait 36410.9: let's do 36410.9. Let's compute 36410 = 3640, 3640.9=327.6, sum is 3640+327.6=3967.6. Now, 3967.6 is closer to 4000 than to 3300 or 4400. Wait, but let's check the options again. Wait, maybe I miscalculated. Wait, 36410.9: 36410=3640, 3640.9=327.6, total 3967.6. So the closest option is 4000? Wait, but let's check with another estimation. 364 is approximately 360, 10.9 is approximately 11. 36011=3960, which is about 4000. So the answer should be 4000? Wait, but let's check the options again. Wait, maybe I made a mistake in the problem. Wait, the options are 3000, 3300, 4000, 4400. So 3967.6 is closest to 4000.

Answer:

4000