Math Problem : CC.3 Number and cost price of apple

I purchased some apples at a certain cost price.

When I sell all apples at 80 yen per piece, there are 500 yen loss and I sell all at 100 yen per piece, there are 1500 yen profits.

How many pieces did I purchase and how much is the cost price per piece ?







Answer
100 pieces 
85 yen

Solution
Comparing selling at 80 yen per piece and selling at 100 yen, there comes out a difference of 100 - 80 = 20 yen.

What there are 500 yen loss by selling at 80 yen per piece and are 1500 yen profits by selling at 100 yen per piece means that there are 1500 + 500 = 2000 yen deference coming out in all. 

The difference is 20 yen per piece and is 2000 yen in all. 

That means that the number of apples purchased is 2000/20 = 100 pieces.

Loss per piece is calculated by 500 /100 = 5 yen. 

Therefore the cost price of an apple is 80 + 5 = 85 yen.