Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 6 Algebra
Problem

1) Larry tells his friend he has a bag containing 4 types of marbles: cat's eye, clear, cloud, and corkscrew. He says that 1/9 of the marbles are corkscrew, 2/9 are clear, and 5 are cloud. What is the fewest number of cat's eye marbles that could be in the bag?

2) Mira's friend is having a birthday this month, but Mira always forgets the exact date. Mira's friend reminds her that 1/3 of the birth date plus 52 equals two times as much as the birth date. What day is her friend's birthday?

3) A group of friends are renting a bus to attend a convention. The company charges a flat rate for a rental, regardless of the number of people using the bus. Fifteen people are planning on attending and want to split the cost evenly. If they get 9 more people they can reduce the cost of the rental by $4.50 per person. How much does it cost to rent the bus?

Problem

4) Beck and Caleb live by an apple orchard. Beck picks 51 apples and Caleb picks 11. Starting the next day, Beck eats 2 of his apples every day, while Caleb picks 3 more every day. How many days until Caleb has more apples than Beck?

5) Mei surveys her classmates for the sports they like. She makes a Venn diagram of her results. There are 616 students at her school. Assuming her survey is an accurate representation of the entire school, how many students like baseball?