WASHINGTON STATE MATHEMATICS COUNCIL -1997 MIDDLE SCHOOL MATH OLYMPIAD

SEVENTH GRADE MEASUREMENT -SCHOOL ___________________________ TEAM_______

1. What is the difference in area between a rectangular field 70 meters by 80 meters and that of a square field with the same perimeter?

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. The dimensions of a rectangle are 20 centimeters by 30 centimeters. If the longer dimension is increased by 20% and the shorter side is decreased by 15%, What is the area of the new rectangle?

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

5. 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?