Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 8 Algebra

Problem
1) Joni is watching her baby sister stack blocks and has discovered that there's an actual pattern! What is a formula that would allow you to compute how many blocks there are in the nth tower?
2) Nancy took and exam which had 26 problems. Her mom told her she would pay her $0.99 for each problem she got right, but Nancy would have to pay her mom $0.61 for each problem she got wrong. If Nancy earned $8.14 for her work on the test, how many problems did she get right?

3) I'm a mystery number. If you multiply me by 3 and then add 4 the result is the same number if you first add 3 to me and then multiply the result by 4. Write an equation to represent this problem. Then find the mystery number.

4) A7 + B13 = 8991
What is A + B if both fractions are positive?

5) Sandy was scuba diving and exploring under an overhanging rock shelf. She lost track of time and realized just in time that she was almost out of air. Her location is as shown on the diagram. If she has 2.1 cubic feet of air left and she uses it at a rate of 0.7 cubic feet per minute, how fast does she have to swim along the shortest path to arrive safely on the surface? Express your answer rounding up to the nearest foot per minute to make sure she makes it.