Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 7 Algebra
Problem
1) Greg's father is 40 years old and Greg is 14 years old this year. Greg notices that each year the ratio of his age to his father's age gets smaller. In how many more years will that ratio be 1:2 or 1/2?

2) Sally usually gets $10 a week for her allowance. Sally asks her parents to change her allowance so that she gets 1 penny on the first day and on each next day double the amount of the previous day. Her parents agree to pay her in pennies for two weeks. Her parents want to know at the end of the two weeks which allowance is better for her and how much better? Compute the difference between the two allowances at the end of the two weeks.

3) A batch of brownies uses 3 eggs and weighs 25 oz. A cake takes 4 eggs and weighs 35 oz. If Wanda has 22 eggs and enough of all the other ingredients how many batches of brownies and how many cakes should she make so that the total weight of baked goods is as large as possible?

Problem
4) Over five years, Lady Simone wishes to give $1,000,000 to her favorite charity. Her plan is to give them more each year. The last or fifth year will be the biggest donation. The fourth year she will give 1/10 what she gives the fifth year. The third year she will give 1/10 what she gives the fourth year. If this pattern continues how much will she give the last year to the nearest dollar?
5) The table shows some data on sales of tickets for a charity event. Paul assumes the data is linear. If that is true, what is the price of 9 tickets?