Question

The owner of a soybean farm raises guinea hens for food and insect control. Guinea hens will eat grasshoppers and other insect pests and ticks. They also act as a "watchdog" by making a lot of noise when intruders approach their territory. The farmer allows the hens free range in his fields during the day and provides roosts for them at night. You may make these assumptions: ∙

1. The farmer lives on 1 hen/day for a year.
2. 1 hen eats 25 grasshoppers/day.
3. 1,000 grasshoppers have a mass of 1 kg.
4. 1 grasshopper requires about 30 g of soy/yr.
6. 1 human requires about 600 grasshoppers/day.
7. dry soybeans have about 3.3 cal/g.

Required:
a. Calculate the number of grasshoppers a hen needs per year.
b. How many grasshoppers are needed for a year's supply of hens for the farmer each year?
c. What is the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year?
d. How many kilograms of soybeans are needed to feed all the grasshoppers for one year?

Answer 1

a. A hen needs 9,125 grasshoppers per year

b. 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year

c. The total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year 3330.625 kg

d. 99918.750 kg of soybeans are needed to feed all the grasshoppers for one year.

Explanation:

a. To calculate the number of grasshoppers a hen needs per year.

There are 365 days days in a year.

From the question, 1 hen eats 25 grasshoppers/day

If 1 hen eats 25 grasshoppers per day, then

1 hen will eat 25 × 365 grasshoppers per year

25 × 365 = 9125

Hence, a hen needs 9,125 grasshoppers per year.

b. To determine how many grasshoppers are needed for a year's supply of hens for the farmer each year

From the question, The farmer lives on 1 hen/day for a year.

That is, for a year, the farmer lives on 365 × 1 hen = 365 hens

Now, we will determine how many grasshoppers 365 hens will need for a year.

Since, a hen needs 9,125 grasshoppers per year

Then, 365 hens will need 365 × 9125 grasshoppers per year

365 × 9125 = 3330625 grasshoppers

Hence, 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year.

c. To determine the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year

From the question, 1,000 grasshoppers have a mass of 1 kg.

That is, 1,000 grasshoppers have a mass of 1000 g

(NOTE: 1000g = 1kg)

If 1,000 grasshoppers have a mass of 1000 g

Then, 1 grasshopper will have a mass of (1 × 1000) /1000 = 1 g

From b., the total number of grasshoppers needed to feed all the hens for one year is 3,330,625 grasshoppers.

Now, we will determine the mass of 3,330,625 grasshoppers

1 grasshopper have a mass of 1 g

∴ 3,330,625 grasshoppers will have a mass of (3,330,625 × 1) / 1 = 3,330,625 g

Now, we will convert this to kilograms (kg)

If 1000 g = 1 kg

Then, 3,330,625 g = (3,330,625 × 1) / 1000 = 3330.625 kg

Hence, the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year 3330.625 kg.

d. To determine how many kilograms of soybeans are needed to feed all the grasshoppers for one year

From the question, 1 grasshopper requires about 30 g of soy/yr

From b., 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year

If 1 grasshopper requires about 30 g

Then, 3,330,625 grasshoppers will require (3,330,625 × 30) / 1 = 99918750 g of soy/yr

Now, we will convert this to kilograms

If 1000 g = 1 kg

Then, 99918750g = (99918750 × 1) / 1000 = 99918.750 kg

Hence, 99918.750 kg of soybeans are needed to feed all the grasshoppers for one year.