Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 8 Algebra

Problem
1) Emil cooks 64 hotdogs for a barbeque. He uses 5 packages of hotdogs plus 4 hotdogs left over from a meal earlier in the week. A friend wonders how many hotdogs were in a package. If x is the number of packages and h is the number of hotdogs, write an equation that could be used to answer the wondering.
2) Each camp counselor at Camp Wallaby walked 6 miles for health and fitness activity. Each camper walked 2 miles. The camp leader paid $0.50 into a Fun Day account for every mile walked. They raised $48. If the ratio of camp counselor to camper is 1 to 13, how many campers are at Camp Wallaby?
3) Two teams enter a contest that has two parts to it. In part A all problems are worth the same number of points, and in Part B problems all problems are worth the same number of points. The Bulldogs score 71 points. The Rams score 72 points. The captain of the Bulldogs finds out that her team answered 9 problems in Part A correctly and 5 problems in Part B correctly. The Rams answered 11 problems in Part A correctly and 4 problems in Part B correctly. What are the Part A problems worth? (If you're stuck, find a way of writing 1 point in terms of A and B.)
4) A biologist studies an insect colony with an initial population of 50 insects. She notices that every three weeks after a new generation is born the population has doubled. What was the difference between the population size after the fourth generation and the population size after the sixth generation?

5) The table shows some data about the number of students enrolled at a junior high. A line fits the data well for the data shown. If the line is accurate, what is the enrollment for 2015?