anonymous
  • anonymous
Wheat contains about 2.5 kcal per gram, and the average U.S. male consumes 2500 kcal per day. How many hectares of wheat are needed to support one average U.S. male for a year, assuming that 30 percent of his caloric intake is from wheat?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
How many grams of wheat per hectare?
anonymous
  • anonymous
3000
anonymous
  • anonymous
Ok, you can start by multiplying 2500 kcal/day by 365.25 days/year by 30/100 to get kcal per year from wheat.

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anonymous
  • anonymous
Divide that by 2.5 kcal/g to get grams of wheat. Then divide that by 3000 grams/hectare to get the number of hectares.
anonymous
  • anonymous
I'm confused with the first and second step, explain please?
anonymous
  • anonymous
Kilocalories per year from wheat = \[\large 2500 \frac{kcal}{\cancel{day}} \times 365.25 \frac{\cancel{day}}{year} \times \frac{30}{100}\]
anonymous
  • anonymous
We're ultimately trying to get the number in units of hectares per year, so I need all the other units to cancel out.
anonymous
  • anonymous
I got this huge number as the answer "273937.5"
anonymous
  • anonymous
Good, that should sound reasonable for grams of wheat needed for an entire year.
anonymous
  • anonymous
Kilocalories per year from wheat divided by 2.5 kcal/g = grams of wheat. \[\large 273937.5 \frac{\cancel{kcal}}{year} \times \frac{grams-of-wheat}{2.5 \cancel{kcal}}\]
anonymous
  • anonymous
What I don't get is where you got "365.25" from?
anonymous
  • anonymous
365.25 = average number of days in a year (to account for possible leap-years).
anonymous
  • anonymous
Could we use 365 instead of the .25 at the end?
anonymous
  • anonymous
Sure, it didn't specify whether it was for a leap-year or not, so you may choose to have your answer for a normal year.
anonymous
  • anonymous
The precision of these numbers is pretty low anyway, so leaving off the .25 shouldn't make a difference.
anonymous
  • anonymous
oh okay, I think i got it. Thanks! :)
anonymous
  • anonymous
Let me know what you get as your final answer.
anonymous
  • anonymous
I got 684375
anonymous
  • anonymous
Hmmm, what steps did you do after getting 273937.5?
anonymous
  • anonymous
I went back and changed the number of days in year to 365. therefore i times that by 2.5 and got 684375
anonymous
  • anonymous
No, you have to divide the number of kcal by 2.5 kcal/g to get grams
anonymous
  • anonymous
See how the 2.5 kcal were in the denominator to cancel it with the kcal on top?
anonymous
  • anonymous
This is why you have to include units in your calculations to see whether to multiply or divide to cancel out the units you don't want.
anonymous
  • anonymous
soo 109500?
anonymous
  • anonymous
Right, now what's the next step? What are the units of that number, 109500? That will guide you.
anonymous
  • anonymous
Umm, is it kg of wheat per hectare?
anonymous
  • anonymous
Dividing kcal/year by kcal/g = grams/year. Why did you say kg? I'm curious. .. . Are you sure its 3000 grams per hectare and not 3000 kg per hectare? 3000 grams per hectare seems kinda small.
anonymous
  • anonymous
Haha, I'm very sorry. I'm not learning in APES at all so I'm just straight up dumb at this subject.
anonymous
  • anonymous
What is 'APES?'
anonymous
  • anonymous
AP Environmental Science
anonymous
  • anonymous
Ah, well, I hate to be the bearer of bad news, but this unit conversion stuff is the easy part of the course.
anonymous
  • anonymous
Yeah.. Well that just tells you how bad I am at math in general.
anonymous
  • anonymous
This can be a tricky topic for people, but that's why I stress always including the unit with the number and always thinking, "how do I make the units I don't want cancel out leaving me only the units I do want?" If you write it out and cancel the units like I have been showing you, it practically solves itself.
anonymous
  • anonymous
So, do we have a confirmation of whether a hectare is 3000 grams of wheat, or is it 3000 kilograms? (It makes a big difference).
anonymous
  • anonymous
Dude, you're awesome. I will use your tip. Thanks a bunch! It says 3000 kg of wheat per hectare
anonymous
  • anonymous
Ok, so the 109500 number is in grams per year. Divide that by 1000 g/kg to get the number in kg.
anonymous
  • anonymous
I got 109.5
anonymous
  • anonymous
109.5 what? What are the units?
anonymous
  • anonymous
The units should be kg/year. Divide by 3000 kg/hectare to get hectares per year.
anonymous
  • anonymous
So divide 109.5 by 3000 and I will get .0365 kg/hectare per year?
anonymous
  • anonymous
I think that should be the right answer. Interesting number, aye? What would it be per day?
anonymous
  • anonymous
uhh, is it 13.3225 per day?
anonymous
  • anonymous
If it is 0.0365 kg/hectare per year and a year has 365 days, then you divide by 365 days per year to get the number per day. Also note that a hectare = 100 acres.
anonymous
  • anonymous
OHHH.. so 1e-4?
anonymous
  • anonymous
Right, so since there are 100 acres in a hectare, and it takes 0.0001 hectares of wheat per day to feed a dude, that's 0.01 acre of wheat per day to feed the average U.S. male.
anonymous
  • anonymous
For additional practice in this method, try this simpler example: Convert 55 miles per hour into feet per second. (show your work).

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