2 winners in May Math Mania

There were two winners in the final Math Mania contest of the 2005-06 school year. Emily Burghoff and Claire Meyer of St. Louis got all six correct answers for the May questions.

You'll remember that Math Mania creator Amy Ruzicka asked one of her Webster University math professors to come up with the May questions. Last month, Ms. Ruzicka graduated with her master's degree in math education.

Dr. Andrea Rothbart of Webster put together six varied math puzzlers for May.

The May questions required a variety of different calculations. But, Emily and Claire were up to the task.

For getting all the answers correct, Emily and Claire will receive $10 Borders' gift certificates.

This summer, Ms. Ruzicka is taking a vacation from her duties as a teacher at St. Gabriel Catholic School and as creator the Math Mania feature.

But, she's promised to bring back the fun math feature in the fall. The first set of questions will be in the September edition of Young Saint Louis.com. Watch for it!!!

Here are the answers to Dr. Rothbart's May questions:

1. A round pizza with diameter 16 inches is placed on a circular platter whose diameter is 20 inches. What percentage of the plate is occupied by the pizza?
   
   ANSWER: The area of the pizza is pi(16) . And the area of the plate is pi(20). The first area is 64% of the second area.
   
   
2. Of 600 apples harvested, every third apple was too small, and every fourth apple was bruised. The remaining apples were perfect. How many perfect apples were there?
   
   ANSWER: 300 perfect apples. 200 were too small, 150 were bruised and 50 were both. So 600 - (200 + 150) + 50 = 300.
   
   
3. A set of 5 positive integers satisfies all of the following: Their average is 5; their median is 5; and their only mode is 8. What is the difference between the largest and smallest numbers in the set?
   
   ANSWER: The difference is 7. The numbers must be 1, 3, 5, 8, 8.
   
   
4. If a 2-inch cube of silver is worth $400, how much is a 5-inch cube of silver worth? (Note: a 2-inch cube is a 2-inch by 2 inch by 2-inch cube.)
   
   ANSWER: $6250. Solve 8: 400 as 125: x
   
   
5. If the number x is 50% larger than the number z, and the number y is 25% larger than the number z, then x is what percent larger than y?
   
   ANSWER: 20%; If x = (3/2)z and y = (5/4)z then x:y as 6:5.
   
   
6. Last Christmas, Mrs. Ruzicka gave each of her nephews the same amount of money - namely as many dollars as she has nephews, and she gave each of her nieces the same amount of money - namely as many dollars as she has nieces. If Mrs. Ruzicka has more nieces than nephews and she gave away a total of $169, how many nephews does she have and how many nieces?
   
   ANSWER: 12 nieces and 5 nephews. 169 = 12 + 5.