A farmers buys n sheep at #a each .When taking the sheep to the market ,8 of them lost. if the farmer sells the remaining of them at #b each and makes no profit overall,what is the relation between a,b and n?
cost: a*n
revenue: b(n-8)
since profit=0, cost=revenue: an = b(n-8)
Ertettrty
To determine the relation between a, b, and n, we can start by calculating the total cost and the total selling price.
1. Total cost: The farmer buys n sheep at #a each, so the total cost of purchasing n sheep would be:
Total Cost = n * a
2. Total selling price: After losing 8 sheep, the farmer sells the remaining ones at #b each. The total selling price can be calculated accordingly:
Total Selling Price = (n - 8) * b
Since the farmer makes no profit overall, the total selling price should be equal to the total cost. Therefore, we can set up the following equation:
(n - 8) * b = n * a
Now, let's simplify and rearrange the equation to find the relation between a, b, and n:
nb - 8b = na
na - nb = -8b
n(a - b) = -8b
Finally, the relation between a, b, and n is:
n = -8b / (a - b)
To find the relation between a, b, and n, we need to analyze the information given in the question.
Let's break down the information:
1. The farmer buys n sheep at #a each.
2. On the way to the market, 8 sheep are lost.
3. The farmer sells the remaining sheep at #b each.
4. The farmer makes no profit overall.
From point 4, we can deduce that the farmer sells the sheep at the same price or less than the buying price since there is no profit. This means that #b ≤ #a.
Now, let's calculate the cost of buying n sheep at #a each. The cost is given by the equation:
Cost = n × #a
After losing 8 sheep, the farmer is left with (n - 8) sheep. The revenue from selling these remaining sheep at #b each is given by the equation:
Revenue = (n - 8) × #b
Since there is no profit overall, the cost and the revenue should be equal. Therefore, we can equate these two equations:
n × #a = (n - 8) × #b
Now, let's simplify this equation to find the relationship between a, b, and n:
#a × n = #b × (n - 8)
Dividing both sides of the equation by n yields:
#a = #b × (n - 8) / n
Thus, the relationship between a, b, and n is:
#a = #b × (n - 8) / n, where #b ≤ #a