Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 7 Number Sense
Problem
1) Jessica is camping with her family and needs to get water for the camp. She needs 11⁄2 gallons. She has a pot that holds 5/8 gallon. The spring where she gets water is 1/5 mile from camp. How many miles will she walk while getting the water using only the 5/8 gallon pot? Express your answer as a mixed number.

2) The prime factors of one number are 2, 3, and 7. A second number has the prime factors 2, 7, and 11. If their least common multiple is 9702 what is the smallest the first number could be?
3) At the summer carnival there is a game of chance. You pay $5.00 to play a single game. A game consists of one toss at the target. If you hit the target you win $11.00. If you miss you get $0.00. What is the fewest number of games you can play and break even? (Meaning the carnival didn't gain or lose any money to you).

Problem
4) Jorrie is an ambitious girl. She has decided that by the time she is 35 she will retire and will live off of the interest of her considerable fortune. The first year of her retirement she wants the interest to be $3.3x105. She will spend 2/3 of the interest, and put the other 1/3 back into her investment. If she earns 5% per year on her investment, how much should her investment be worth at the beginning of the second year of retirement? Express your answer to the nearest dollar without using scientific notation.

5) In the expression below place minus signs and parentheses on the left hand side of the equal sign to create a true equation.
3       4       5       6 = 2