__Category__: Algebra"Published in Newark, California, USA"

Aling Etang bought several dozen eggs at PHP 600. Because of poor storage, 2 dozens were spoiled and had to be thrown away. Nonetheless, she realized a profit of PHP 154 by charging PHP 3 more than she paid per dozen. How many dozen eggs did she buy?

__Solution__:

The given word problem is about money and investment problem with profit, of course where she thrown 2 dozens of eggs but she earned a profit by charging more than she paid per dozen in order to save her capital or investment from loss. Let's analyze the problem as follows

Let x = be the price of a dozen of eggs, in PHP

y = be the number of dozens of eggs

From the first word statement, "Aling Etang bought several dozen eggs at PHP 600", the working equation will be

From the next word statement, "Because of poor storage, 2 dozens were spoiled and had to be thrown away", the working equation will be

From the next word statement, "....by charging PHP 3 more than she paid per dozen," the working equation will be

The overall working equation for this problem is

Profit = Total Amount Sold - Total Amount Invested

but

and

The above equation becomes

Divide both sides of the equation by -2, we have

Multiply both sides of the equation by x, we have

Use Quadratic Formula to solve for the value of x, we have

To calculate the price of a dozen of eggs, choose the positive sign as follows

Therefore, the price of a dozen of eggs is PHP 10.

Consider the first equation

if x = 10, then

Therefore, Aling Etang bought

**60 dozens**of eggs.

__Note__: PHP means Philippine Pesos and the prices mentioned in the word problem above was in 1985.