Answer:
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.
Step-by-step 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.
