Final answer:
To find the mass of quail eggs that the farmer would need to weigh out in order to have the same number of eggs as 32.0 pounds of chicken eggs, we conversion from pounds to kilograms and used the conversion factor to convert the mass from kilograms to quail eggs.
Step-by-step explanation:
To find the mass of quail eggs that the farmer would need to weigh out in order to have the same number of eggs as 32.0 pounds of chicken eggs, we need to convert the weight from pounds to kilograms. We can then use the conversion factor to convert the mass from kilograms to quail eggs.
First, we need to convert 32.0 pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram, so we can multiply 32.0 pounds by the conversion factor:
32.0 pounds × (1 kilogram / 2.20462 pounds) = 14.51526 kilograms.
Next, we need to convert the mass from kilograms to quail eggs. We can use the fact that the number of eggs is proportional to the mass. If the mass of the chicken eggs is 14.51526 kilograms, and the mass of the quail eggs is x kilograms, then the number of quail eggs is proportional to x:
Number of quail eggs / Number of chicken eggs = x / 14.51526.
Since we want the number of quail eggs to be the same as the number of chicken eggs, we can set this ratio equal to 1:
1 = x / 14.51526.
Now, we can solve for x by multiplying both sides of the equation by 14.51526:
x = 14.51526.
The mass of quail eggs that the farmer would need to weigh out to have the same number of eggs as 32.0 pounds of chicken eggs is 14.51526 kilograms.