A farmer bought 3 1/2 dozen eggs. Fourteen were bad.
a) what fraction were bad?
b) What percentage were good?
c) If the eggs cost $18.00 per dozen. How much did he pay for the eggs?
well, there are 42 eggs in total.
Now work out the rest, based on that.
a) To find the fraction of eggs that were bad, we need to know the total number of eggs.
3 1/2 dozen eggs can be calculated as follows:
3 dozen + 1/2 dozen = 3 + 1/2 = 3 1/2.
Now, let's convert 3 1/2 dozen to a fraction:
3 1/2 = 7/2.
To find the total number of eggs, we multiply the number of dozens by 12 (since there are 12 eggs in a dozen), and then add the remaining fraction:
Total number of eggs = (7/2) x 12 = 84/2 = 42.
Now, we can find the fraction of eggs that were bad. Given that 14 eggs were bad:
Fraction of eggs that were bad = 14/42 = 1/3.
So, the fraction of eggs that were bad is 1/3.
b) To find the percentage of eggs that were good, we subtract the fraction of eggs that were bad from 1 (since 1 represents the whole or 100%).
Percentage of eggs that were good = (1 - 1/3) x 100 = (2/3) x 100 = 66.67%.
Therefore, 66.67% of the eggs were good.
c) To find out how much the farmer paid for the eggs, we need to calculate the cost per egg. We're given that the eggs cost $18 per dozen.
Cost per egg = $18 per dozen.
Since there are 12 eggs in a dozen, the cost per egg can be calculated as follows:
Cost per egg = $18 / 12 = $1.50.
As we found earlier, the total number of eggs is 42. So, the total cost of the eggs can be calculated as:
Total cost of eggs = Cost per egg x Total number of eggs = $1.50 x 42 = $63.
Therefore, the farmer paid $63 for the eggs.