Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 8 Algebra
Problem
1) How many integers satisfy (n - 4)(n + 6) ≤ 0?
2) Jack's science and math book together weigh 8 pounds. His social studies and science books together weight 11 pounds. His math and social studies books together weight 9 pounds. How much does the science book weigh by itself?

3) What is the sum of the next two outputs in the table below?

Problem
4) For what value of k do the lines y = x⁄4, 3x + 4y = 32, and y = kx - 14 all intersect in exactly one point?
5) A stamp collector has a huge supply of old 4-cent stamps and 7-cent stamps. What is the greatest amount of postage that cannot be made up using these stamps? (For instance 25 cents can be made with one 4-cent stamp and three 7-cent stamps.)