## anonymous 4 years ago 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?

1. anonymous

How many grams of wheat per hectare?

2. anonymous

3000

3. 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.

4. 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.

5. anonymous

I'm confused with the first and second step, explain please?

6. anonymous

Kilocalories per year from wheat = $\large 2500 \frac{kcal}{\cancel{day}} \times 365.25 \frac{\cancel{day}}{year} \times \frac{30}{100}$

7. 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.

8. anonymous

I got this huge number as the answer "273937.5"

9. anonymous

Good, that should sound reasonable for grams of wheat needed for an entire year.

10. anonymous

Kilocalories per year from wheat divided by 2.5 kcal/g = grams of wheat. $\large 273937.5 \frac{\cancel{kcal}}{year} \times \frac{grams-of-wheat}{2.5 \cancel{kcal}}$

11. anonymous

What I don't get is where you got "365.25" from?

12. anonymous

365.25 = average number of days in a year (to account for possible leap-years).

13. anonymous

Could we use 365 instead of the .25 at the end?

14. 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.

15. anonymous

The precision of these numbers is pretty low anyway, so leaving off the .25 shouldn't make a difference.

16. anonymous

oh okay, I think i got it. Thanks! :)

17. anonymous

18. anonymous

I got 684375

19. anonymous

Hmmm, what steps did you do after getting 273937.5?

20. anonymous

I went back and changed the number of days in year to 365. therefore i times that by 2.5 and got 684375

21. anonymous

No, you have to divide the number of kcal by 2.5 kcal/g to get grams

22. anonymous

See how the 2.5 kcal were in the denominator to cancel it with the kcal on top?

23. 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.

24. anonymous

soo 109500?

25. anonymous

Right, now what's the next step? What are the units of that number, 109500? That will guide you.

26. anonymous

Umm, is it kg of wheat per hectare?

27. 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.

28. anonymous

Haha, I'm very sorry. I'm not learning in APES at all so I'm just straight up dumb at this subject.

29. anonymous

What is 'APES?'

30. anonymous

AP Environmental Science

31. anonymous

Ah, well, I hate to be the bearer of bad news, but this unit conversion stuff is the easy part of the course.

32. anonymous

Yeah.. Well that just tells you how bad I am at math in general.

33. 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.

34. 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).

35. anonymous

Dude, you're awesome. I will use your tip. Thanks a bunch! It says 3000 kg of wheat per hectare

36. anonymous

Ok, so the 109500 number is in grams per year. Divide that by 1000 g/kg to get the number in kg.

37. anonymous

I got 109.5

38. anonymous

109.5 what? What are the units?

39. anonymous

The units should be kg/year. Divide by 3000 kg/hectare to get hectares per year.

40. anonymous

So divide 109.5 by 3000 and I will get .0365 kg/hectare per year?

41. anonymous

I think that should be the right answer. Interesting number, aye? What would it be per day?

42. anonymous

uhh, is it 13.3225 per day?

43. 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.

44. anonymous

OHHH.. so 1e-4?

45. 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.

46. anonymous

For additional practice in this method, try this simpler example: Convert 55 miles per hour into feet per second. (show your work).