Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 7 Algebra
Problem
1) Mr. Smith and Mr. Jones have decided to separate their property by placing a fence along the property line. They ordered enough fence posts so that the fence would have posts placed 8 feet apart. However, five of the posts were not usable. They were still able to put the fence up by placing the remaining posts 10 feet apart. How many fence posts did they originally order?

2) Kate creates a new sequence of numbers: 2, 3, 5, 25, 200 .... After the first three terms, 2, 3, and 5, each new term is found by adding the first two of three previous terms and then multiplying this sum by the final previous term. For example, the fourth terms is (2+3)(5) = 25. Now, Carrie uses Kate's technique but starts with new terms (a, 4, 6) to create a new sequence: a, 4, 6, (a+4)(6), ..... If the fifth term of Carrie's sequence is 300, what is the fourth terms of Carrie's sequence?

Problem

3) Mina's current cell phone plan costs $29.99 a month plus $0.029 a minute. She is thinking about changing to a new plan that costs $49.99 a month but doesn't charge anything per minute. How many minutes can she talk per month on her current plan to break even with the second plan? Round your answer to the nearest minute.

4) The first three of a sequence of growing dot figures is shown. If the sequence continues in the growing pattern, how many dots would be in the 100th figure?
5) Carlos is training for a down hill run. He has several friends timing at different spots along the trail and they all start their watches at the same time on a signal when he starts his descent. The table shows the results of Carlos' elevation in feet versus time in seconds and it turns out the data is linear. How high up to the nearest foot was Carlos when he started his descent?