A market woman buys n eggs at the rate of twelve eggs for sixty naira. Eight of the eggs were brokensi she sold the remaining at the rate of four eggs for twenty four naira and made a profit of twelve naira. How many eggs did she buy?
Let's assume the market woman bought x eggs.
According to the information given, she bought the eggs at a rate of 12 eggs for 60 naira. Therefore, the cost of x eggs is (60/12) * x = 5x naira.
Out of the x eggs, 8 eggs were broken. Therefore, she sold (x - 8) eggs.
She sold 4 eggs for 24 naira. Therefore, she sold (24/4) * (x - 8) = 6 * (x - 8) eggs for 5x + 12 naira.
From the above information, we can create an equation: 6(x - 8) = 5x + 12
Expanding the equation gives 6x - 48 = 5x + 12
Subtracting 5x from both sides of the equation gives x - 48 = 12
Adding 48 to both sides of the equation gives x = 60
Therefore, the market woman bought 60 eggs. Answer: \boxed{60}.
Let's assume that the market woman bought x eggs.
According to the given information, the market woman buys twelve eggs for sixty naira. So, the cost price of one egg is 60/12 = 5 naira.
Out of the total eggs bought, eight were broken. So, she had (x - 8) eggs remaining.
She sold the remaining eggs at the rate of four eggs for twenty-four naira. So, the selling price of one egg is 24/4 = 6 naira.
She made a profit of twelve naira. We can say that her selling price is twelve naira more than her cost price for the remaining eggs.
Selling price - Cost price = Profit
(6 * (x - 8)) - (5 * (x - 8)) = 12
6x - 48 - 5x + 40 = 12
x - 8 = 12
x = 12 + 8
x = 20
Therefore, the market woman bought 20 eggs.
To solve this problem, let's break it down into smaller steps:
Step 1: Calculate the cost of 12 eggs
The market woman buys 12 eggs for 60 naira, so the cost of one egg is 60 naira divided by 12, which equals 5 naira.
Step 2: Calculate the cost of 8 broken eggs
The cost of one egg is 5 naira, so the cost of 8 broken eggs is 5 naira multiplied by 8, which equals 40 naira.
Step 3: Calculate the total cost of the remaining eggs
The market woman bought n eggs in total, and 8 were broken. Therefore, the remaining eggs would be n minus 8.
Step 4: Calculate the selling price of the remaining eggs
The market woman sold the remaining eggs at a rate of 4 eggs for 24 naira. So the selling price of one egg is 24 naira divided by 4, which equals 6 naira.
Step 5: Calculate the total selling price of the remaining eggs
The selling price of one egg is 6 naira, so the total selling price of the remaining eggs is 6 naira multiplied by (n - 8).
Step 6: Calculate the profit
The market woman made a profit of 12 naira. Therefore, the total selling price must be the cost price (total cost of the remaining eggs) plus the profit.
Now that we have all the information, let's put it together into an equation:
Total selling price = Cost price + Profit
6(n - 8) = 5(n - 8) + 12
Solving this equation will give us the value of 'n', which represents the total number of eggs the market woman bought.