Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 5 Algebra
Problem
Solution
1) Mary is having a sleepover. She can have no more than 8 friends come. Her parents tell her they will buy a half gallon of vanilla ice cream and a 2 liter bottle of root beer to make root beer floats. How many friends should she invite if she wants everyone to get a root beer float, including herself, made with a scoop of ice cream and 1/4 liter of root beer? She knows there are at least 10 scoops of ice cream in the half gallon. 1. Since there are 10 scoops of ice cream in the half gallon, the ice cream is no problem. It can accommodate 10 friends, including herself.
2. The 2 liter bottle of root beer can make 8 floats.
3. If she includes herself, she can invite 7 friends.
2) Mrs. Steews notices if 9 math club members come to practice she can pass out 5 Hershey kisses to each one with some left over. If 12 show up she can pass out at 4 to each member with some left over. If only 7 club member show up how many can she pass out to each member? 1. If she passes out 5 kisses to each of 9 members with some left over she has between 46 and 49 kisses.
2. If she passes out 4 kisses to each of 12 kisses with some left over she has between 49 and 51 kisses.
3. The only number of kisses that fits both these limits is 49
4. Dividing this number by 7 means she can pass out 7 kisses to each member.
3) Rory knows he is 8 inches shorter than his sister. He's figured out that his height in inches is 7/8 her height in inches. How tall is he in inches? 1. If he is 7/8ths of his sister's height then what remains is the fraction 1/8.
2. This fraction of his sister's height is 8 inches.
3. Rory's sister's height is
    Let h be his sister's height.
    Then h/8 = 8 inches.
    h = 8 x 8 = 64 inches.
    He is 8 inches shorter than this which is 56 inches.

Problem
Solution
4) Morissa buys a vine that grows very quickly at first. It's 2 feet tall when she plants it. A month later it has reached a length of 10 feet. A month later it has reached a length of 14 feet and a month after that it has reached a height of 16 feet. If this growth pattern continues how long will the vine be in three more months? Give your answer in feet and inches. This is a geometric series where each successive number is multiplied by a factor.
1. Write down a list of the months, the height at the end of that month and the amount the vine grows from the previous month. You should notice a multiplicative factor.
MonthHeight1 month growth
02 ft-
1108
2144
3162
4171
517 1/21/2
617 3/41/4
The multiplicative factor is 1/2.
2. The vine will be 17 feet 9 inches tall.
5) For the 4th of July the Community Center is decorating with balloons arranged around its large gathering room in the pattern: Blue, White, Red, Red, White, White. What will be the color of the 130th balloon in the pattern? 1. The repeating pattern is 6 colors long.
2. Divide the balloon number by this number and the remainder is 130/6 = 21. The remainder is 4.
3. This is the number of the color in the pattern. If that number is 0, then the color is the last one in the pattern.
4. The 130th balloon will be red