WASHINGTON STATE MATHEMATICS COUNCIL - 1997 MIDDLE SCHOOL MATH OLYMPIAD

EIGHTH GRADE ALGEBRAIC SENSE - SCHOOL ___________________________ TEAM_______

1. A number is increased by 50%, then the resulting number is decreased by 40%. The result is 8 less than the original number. What is the original number?

Answer: ________________

2. Mark sets fence posts for a living. He takes a job to enclose a rectangular field 200 feet by 500 feet. Posts are set every 10 feet. He pays his helpers $8.50 per hour for setting each post. Each post costs $3. What is Mark's cost for this job?

Answer: ________________

4. The surface of a solid wooden cube is painted blue. The cube is then cut into smaller cubes, each measuring 1 cu. in. 54 of them have only one face painted blue. What was the volume of the large cube?

Answer: ________________

4. Here are the first three buildings in a series built with cubes. Write an expression that will generate the X^{th} building in this series. ("X" numbers the buildings in the seiries.)

Answer: ________________

4. Consider the infinite sum: 96 + 48 + 24 + 12 + ... where each addend is half the previous addend and the pattern continues without end. The sum of the first ten tearms is 191.8125. Each addition gets you midway from where you are to 192. So the sum gets as close to 192 as you want. Next consider the sum 144 + (-72) + 36 + (-18) + 9 + (-4.5) + ... whose addends are alternately positive and negative and where each addend is (-1/2) times the previous addend. This infinite sum also getsa as close as you want to some number. Find this whole number.

Answer: ________________