WASHINGTON STATE MATHEMATICS COUNCIL - 1997 MIDDLE SCHOOL MATH OLYMPIAD

SEVENTH 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?

2. In one round of a game show the second question is worth twice a much as the first. The third question is worth three times as much as the second. The fourth question is worth four times as much as the third, and the fifth question is worth five times as much as the fourth. The fifth question is worth \$12,000. What is the first question worth?

3. 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?

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?

5. On OTV they have a puzzle game called "Igor's Rules". The purpose is to guess the rule being used by Igor in order to win the prize. Each time Igor is presented with a group of gum-drops and ,using Igor's current rule, Igor sends a certain number of gum-drops. In this round Igor is given 8 gum-drops and sends 6 gum-drops. Igor then receives 15 gum-drops and sends 27 gum-drops. Next Igor is given 25 gum-drops and sends back 57 gum-drops. If Igor is given 44 gum-drops, how many will he send back using the current rule?