Answer to Math Olympiad #2

Problem:

In a stationery store, pencils have one price and pens have another price.  Two pencils and three pens cost 78¢.  But three pencils and two pens cost 72¢.  How much does one pencil cost?

Solution:

By combining both purchases we find that 5 pencils and 5 pens cost 150¢.  Then 1 pencil and 1 pen cost 30¢, or 2 pencils and 2 pens cost 60¢.  Since 3 pencils and 2 pens cost 72¢, 1 pencil costs 12¢.