Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 5 Algebra
Problem
Hint
1) Aaron is making a pattern with tiles.
If he keeps this pattern going, how many tiles will be in figure 20?
1. Write out in a list the number of tiles in each figure:
    5   ___   ___
2. Determine the increment between each figure = ____ tiles.
3. Choose one of these solutions:
Method 1: list the elements
Write out all the elements up to the one you want using the increment you found:
5 ...
    There are ____ tiles in figure 20. 		Method 2: Use the formula for an arithmetic sequence:
AN = A1 + D x (N - 1) where:
A1 is the first term,
AN is the Nth term
(the term you are looking for), and
D is the number that is added to each term
A20 = _____ tiles.
2) It costs a fixed fee to set up a party at the local trampoline gym. After that amount is paid, there is a cost per guest. Based on the table below, how much is the fixed fee to set up a party?
1. The number of added guests in the second column is _____.
2. The increase in cost from the first column to the second is ______
3. The added cost per guest = ________
4. Multiply the number of guests in the first column
    by this added cost per guest = ________
5. Subtract this from the first column to get the fixed cost = ________

Problem
Hint
3) A pile of 30 coins is worth $5.00. There are only quarters, dimes, and nickels in the pile. There are only 2 dimes. How many quarters are there? 1. Subtract from the total worth of the pile the 2 dimes = $_____
This is the amount of money that is in quarters and nickels.
2. There are now ____ coins that are quarters or nickels.
3. This is now a guess-and-check problem. Here's the table:
Guess ## quarters# nickelsTotal
$
11515$4.50
    
    
    
    
4) I'm thinking of a number. If I multiply my number by 12 and then add 2, I get the same result as if I had added 90 to my number. What is my number? Using N for the number,
1. Write the expression for "multiply my number by 12 and then add 2" = ____________.
2. Write the expression for "add 90 to my number" = _______.
3. Set these two expressions equal to each other and solve.
    N = __________

5) Raihana is reading a new book. She just finished 1/3 of the book. She notices that if she reads 60 more pages she will be 1/2 done with the book. How many pages long is the book? 		1. The difference between 1/2 and 1/3 of the book is ____ of the book.
2. If that fraction is 60 pages then the total book is _____ pages.