a market woman buy's n eggs at the rate of 12 eggs for 60naira .8 of the eggs where broken so she sold the remaining at the rate of 4.eggs.for 24 and makes profit of 12 naira. how many eggs did she buy
To solve this problem, we need to break it down into steps and use a bit of algebra.
Let's denote the number of eggs the market woman bought as 'x'.
According to the given information, she bought x eggs at the rate of 12 eggs for 60 naira. This means that the total cost of buying x eggs is (x/12) * 60.
8 of the eggs were broken, so the market woman had x - 8 eggs left.
She sold the remaining eggs at the rate of 4 eggs for 24 naira, which means that the total selling price of the remaining eggs is (x - 8)/4 * 24.
It is mentioned that the market woman made a profit of 12 naira. So, we can set up the following equation:
Total selling price - Total cost = Profit
[(x - 8)/4 * 24] - [(x/12) * 60] = 12
To simplify the equation, we can multiply through by 12 to eliminate fractions:
[(x - 8) * 2] - [(x/12) * 5] = 144
Now, we can further simplify the equation by expanding the terms:
2x - 16 - (5/12)x = 144
To solve for x, we can group the x terms on one side of the equation and the constant terms on the other side:
(2x - (5/12)x) = 144 + 16
Combining like terms:
(24/12)x = 160
Now, let's simplify the left side of the equation:
2x - (5/12)x = (24/12)x - (5/12)x = (19/12)x
Substituting back into the equation:
(19/12)x = 160
To isolate x, we can multiply both sides of the equation by the reciprocal of (19/12), which is (12/19):
x = 160 * (12/19)
Simplifying the right side of the equation:
x ≈ 101.05
So, the market woman bought approximately 101 eggs.