Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 6 Algebra
Problem
Hint
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? 1. Corkscrew and clear account for ____ of the marbles.
2. Cloud and cat's eye marbles account for ____ of the marbles.
3. Since there must be a whole number of cat's eye marbles, compute the minimum number of them that would allow them and cloud marbles to be ____ of the whole = _____ cloud marbles.

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? 		Let D be the birth date.
Solve the equation for D:
    (1/3)D + 25 = 2 x D.
    D = _____

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?		 Let C = the cost of the bus.
1. Then C/15 is the cost per person for 15 people
2. C/24 is the cost per person for 24 people
3. Write an equation for "the cost per person for 15 people is the cost per person for 24 people plus $4.50" and solve.

    C = ______

Problem
Hint
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? 1. Every day the difference between Beck and Caleb's apples decreases by ____ apples.
2. Divide the original difference between their apples by this to find the number of day until they are equal = ____ days.
3. Since we want to know how many days until Caleb has more apples than Beck, you must add one = _____ days.
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?
 1. Add up all the numbers in the baseball circle = ____
2. Add up all the numbers in the total diagram, including the "other" number = ______ students.
    This is the total number of students in her survey
3. Divide 616 by this number of students to get the ratio of total students to students in the survey = _____
4. Multiply this ratio by the number of students in the survey that liked baseball to get the total number of students that like baseball = ______