WASHINGTON STATE MATHEMATICS COUNCIL - 1997 MIDDLE SCHOOL MATH OLYMPIAD

EIGHTH GRADE MEASUREMENT - SCHOOL ___________________________ TEAM_______

1. A group of 20 coins contains only dimes and nickels. If the value of the coins is greater than \$1.40, what is the least number of dimes in the group?

2. We have acquired a recipe for the world famous Mrs. Hansberry's Peanut Butter Cookies. Unfortunately, it is a recipe for commercial use and needs to be modified for our use. Here is a list of the ingredients with their quantities:

 10 gal butter or margarine 10 gal granulated sugar 320 eggs 25 gal sifted flour salt is 1/3 the amount of soda 10 gal peanut butter 10 gal brown sugar 31/3 c vanilla extract 5c soda
 3 t (teaspoons) = 1T (tablespoon) 4 qt = 1 gal (gallon) 8 qt = 1 peck 4 C = 1 qt (quart) 2 C = 1 pt. (pint) 1 C = 8 fl. oz. (fluid ounces) 16 T = 1 C (cup) 4 pecks = 1 bushel

This makes 128 packages with two rows of five cookies stacked three high. If you are going to make four dozen cookies, how many teaspoons of soda will you need?

3. Equilateral triangle TAR sits adjacent to square REST, sharing side RT and not overlapping the square. What is the measure of angle ATE?

4. Debra has 23 coins, 8 quarters and 15 dimes. She exchanges the 8 quarters for the number of dimes equal to the value of the 8 quarters. She also exchanges the 15 dimes for the number of quarters equal to the value of 15 dimes. After these exchanges, how many coins does she have?

5. Two joggers are running around an oval track in opposite directions. One jogger runs around the track in 56 seconds. The joggers meet every 24 seconds. How many seconds does it take the second jogger to run around the track?