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Washington State Math Olympiad
Hints and Solutions
2012 Grade 8 Algebra
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1) Tim is notified that he has a $50 library fine in August. A fee of 20% of the current amount owed is added to the balance on the first of each month. If he does nothing to pay off his fine or incur new fines what will the total fine be in January?
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2) Consider the sequence of numbers that starts with: 2, 5, a, b, 30. Suppose that in this sequence, after the first three terms (2,5,a), each subsequent term is found by adding the
previous three terms. For example, the fourth term is 2+5+a. Using this fact and noting that the fifth term of the sequence is 30, what is the value of b?
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3) Biffy and Scott are hiking off of a mountain from different rest areas. Biffy's descent to the bottom of the trail can be represented by B=500-5t, where B is in yards and t is in
seconds. Scott's descent can be represented by the function S=200-4t, where S is in yards and t is in seconds. If they arrive at the bottom of the trail at the same time, how many
seconds later than Biffy did Scott leave his rest area?
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4) One-fifth of the fence posts around River Park are oak and the rest are pine. Jeremy places reflectors on 1/3 of the pine fence posts. If 231 fence posts in River Park do not have reflectors, how many are oak?
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5) At Park Boat Rentals you can rent a kayak. The rates are given in the table for up to 4 hours of renting. If the table is continued, how much would it cost to rent a kayak for 8
hours?
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