Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 5 Algebra

Problem
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.
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?

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?
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.
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?