Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 8 Algebra

Problem
Hint
1) Leena is descending a flight of stairs. She is one-fifth the way down. If she takes 28 more steps, she will be one-third the way down. How many steps are in the flight of stairs? Let s = the number of steps in the flight of stairs. 28 steps + 15 of the flight of stairs = 13 of the flight
Set up the expression for s and solve.



s = _____
2) The table shows data on the sales of specialty cakes at a local bakery. Assuming the data is linear, what is the price for 12 cakes?
  1. With the number of cakes as the x axis and their price as y, find the slope of the linear equation using the first 2 points:


    Slope = $___________/cake.
  2. Apply this slope to the 12 cake value using the 7 cake data:
    y = $_____________
3) Your friend asks for your help with her project because they know you could finish it in half the time it would take them. Without your help, it would take your friends 30 days to finish the project. Working together, how long will it take to finish the project?
  1. Your friend works at a rate of ____ days/project
  2. You work at a rate of ____ days/project
  3. Let d = the number of days you work together to accomplish the project.
  4. Then (d/____ + d/_____) = 1 project



    d = ______ days.

Problem
Hint
4) Hawk will receive an A in math for the semester if the mean of his test scores is at least a 90. If his first two test scores are as shown in the table, write an inequality for the score Hawk needs on his third test to receive an A for the semester.
Let x = the score of his 3rd test.

(Test1 + Test2 + x) / 3 ≥ 90.
Solve for x:


x ≥ ______
5)
2a + 3b + 4c = 331
a + b = 56
b + c = 78
Solve for b.
Use the second and third equations to express a and c in terms of b and then substitute those expressions back into the first equation and solve for b




b = _____