Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 8 Number Sense
Problem
Hint
1) In the expression below place minus signs "-" and parentheses on the left hand side of the "=" to create a true equation.
Note: 2(4 - 1) = 6 and - (2) = -2, (2-1) = 1.

3   4   5   6 = 3
  1. The problem is that 6. We can't use "+" so make it positive using 2 "-" signs.
  2. Now, if the remainder of the expression can be made to equal to -3, then the total expression will evaluate to +3
  3. Find a way to make the 3 4 5 evaluate to -3 using parentheses and "-" signs:


    The expression is ______________________
2) If 23 x 37 x 104 = 6, then what is k?
        (36)k x 54
  1. First multiply both sides of the equation by (36)k to get the k into the numerator.
  2. Simplify down to find k:




    k = _____

Problem
Hint
3) Ibrahim wants to buy an X-Box elite console that costs $380. His dad says he'll buy it for him with his credit card but Ibrahim has to pay him back. Ibrahim can pay him $10 on the first day of every month. Ibrahim's dad will also charge him 18% annual interest on the unpaid balance at the end of every 12 month cycle (year) so that he can get an idea of how credit cards work. If Ibrahim agrees, how much will he end up paying his dad for the console?
  1. If Ibrahim pays his dad $10 every month, it will take him _______ years and _____ months to pay him back
  2. The interest he will pay is:
    1. End of year 1: _______

    2. End of year 2: _______

    3. End of year 3: ________
  3. The total he pays is ______
4) Athena uses two packs of 500 sheets of paper to make the estimate that one sheet of paper is 4 x 10-3 inches thick. A paper mill produces 5.22 x 106 sheets of paper per day. If all the sheets produced in a day were stacked up, how many feet high would the stack reach? Express your answer in feet without using scientific notation. Multiply the number of sheets by the thickness of one sheet to get the height in inches, then divide by 12.



= _______ feet.

5) The math teacher plays a game of Guess My Number with her class for the last 10 minutes of the period. The students narrow it down to a number between 100 and 500. With 2 minutes left she tells them the square root of the number is a whole number greater than 15 and the square of the square root of the number is a whole number with a 9 as the units digit. What's the number?
  1. √500 = _____, so the square root of the number is between ____ and ____.
  2. Compute the squares of these numbers until you find one that ends in a 9:



    The number is _____