Problem of the Week 26

On a string of 33 pearls, the middle pearl is the largest and most expensive of all.  Starting from one end, each pearl is worth $100 more than the one before, up to the middle.  From the other end, each pearl is worth $150 more than the one before, up to the middle.  The string of pearls is worth $65,000.  What is the value of the middle pearl?

 

Alternate Problem 26

A singer has twice as many pants as pairs of shoes in her wardrobe and three-halves as many T-shirts as pants.  What is the least number of items she can have in her wardrobe in order to make a different shoes, pants, and T-shirt combination for each day of the year.

 

Extension Problem 26

In how many different ways can five-cent and eight-cent stamps be used to make $2.43.  What are the different combinations?