How long will it take the farmer to sell all his chickens?
Farmer has 2100 chickens. He sells
10 chickens at the end of the first week,
20 chickens at the end of the second week,
30 chickens at the end of the third week and so on.
Question: How long will it take the farmer to sell all his chickens?
210 weeks
To find out how long it will take the farmer to sell all his chickens, we need to determine the rate at which the number of chickens sold per week is increasing.
From the information given, we can see that the number of chickens sold per week is increasing by 10 each week. This is an arithmetic sequence with a common difference of 10.
To find the number of weeks it will take to sell all the chickens, we can use the formula for the sum of an arithmetic sequence:
Sum = (n/2)(2a + (n-1)d)
where Sum is the total number of chickens sold, n is the number of terms, a is the first term, and d is the common difference.
Let's solve for n:
Sum = (n/2)(2 * 10 + (n-1) * 10)
2100 = (n/2)(20 + 10n - 10)
2100 = (n/2)(10n + 10)
2100 = (n/2)(10n + 10) / 10
210 = (n/2)(n + 1)
Now, let's solve the quadratic equation:
n^2 + n - 420 = 0
Using the quadratic formula, we can find the roots of this equation:
n = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = 1, and c = -420
n = (-1 ± √(1^2 - 4(1)(-420))) / (2*1)
n = (-1 ± √(1 + 1680)) / 2
n = (-1 ± √1681) / 2
Since the number of weeks must be a positive value, we take the positive root:
n = (-1 + √1681) / 2
n = (-1 + 41) / 2
n = 40 / 2
n = 20
Therefore, it will take the farmer 20 weeks to sell all his chickens.