Question

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?

Answer 1

How many grams of wheat per hectare?

Answer 2

3000

Answer 3

Ok, you can start by multiplying 2500 kcal/day by 365.25 days/year by 30/100 to get kcal per year from wheat.

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

We're ultimately trying to get the number in units of hectares per year, so I need all the other units to cancel out.

Answer 8

I got this huge number as the answer "273937.5"

Answer 9

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

Answer 10

Kilocalories per year from wheat divided by 2.5 kcal/g = grams of wheat.

\[\large 273937.5 \frac{\cancel{kcal}}{year} \times \frac{grams-of-wheat}{2.5 \cancel{kcal}}\]

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

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

Answer 16

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

Answer 17

Let me know what you get as your final answer.

Answer 18

I got 684375

Answer 19

Hmmm, what steps did you do after getting 273937.5?

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

soo 109500?

Answer 25

Right, now what's the next step?

What are the units of that number, 109500?

That will guide you.

Answer 26

Umm, is it kg of wheat per hectare?

Answer 27

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.

Answer 28

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

Answer 29

What is 'APES?'

Answer 30

AP Environmental Science

Answer 31

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

Answer 32

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

Answer 33

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.

Answer 34

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).

Answer 35

Dude, you're awesome. I will use your tip. Thanks a bunch!

It says 3000 kg of wheat per hectare

Answer 36

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

Answer 37

I got 109.5

Answer 38

109.5 what? What are the units?

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

uhh, is it 13.3225 per day?

Answer 43

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.

Answer 44

OHHH.. so 1e-4?

Answer 45

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.

Answer 46

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