Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 8 Algebra
Problem
Hint
1) If 35 = 243 and xy = 625, what is the value of yx?

 Keep taking square roots of 625 until you get to the smallest one. That will give you both x and y
2) A bucket has 10 balls numbered 1,1,2,3,4,4,4,5,6, and 6. If one ball is drawn at random, write an inequality that relates the chance of getting an even number to the chance of getting a multiple of 5? Express in lowest terms.
  1. The probability of getting an even number is __________
  2. The probability of getting a multiple of 5 is ________________
  3. So the inequality is
    ______________________
3) If a=4 in the equations below, what is the value of (d+c+b)a?
 Substitute 4 for a in each expression (the first expression gives you b right away!). You should be able to find c and d.

Problem
Hint
4) How many integers for x satisfy
(x - 11)(x + 3) < 0?
  1. In the first expression, any x below ____ results in a negative number
  2. In the second expression, any x above ____ results in a negative number.

  3. The range for x is _____________________
5) You inherit an unusual stamp collection containing hundreds of 6 and 7-cent stamps. What is the greatest amount of postage that could not be made using a combination of these stamps? (For example, 25 cents postage could be made with three 6-cent stamps and one 7-cent stamp) Here is the table of 6-cent and 7-cent stamp combinations:
# 6-cent stamps
↓ 		# 7-cent stamps
0 1 2 3 4 5 6
0 0 7 14 21 28 35 42
1 6 13 20 27 34 41 48
2 12 19 26 33 40 47 54
3 18 25 32 39 46 53 60
4 24 31 38 45 52 59 66
5 30 37 44 51 58 65 72
6 36 43 50 58 65 72 79
7 42 49 56 63 70 77 84
By examining this table you should be able to find the largest sum that cannot be made with 6-cent and 7-cent stamps = ________