Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 8 Algebra
Problem
Hint
1) A bowl of candies sit on the counter. Jerry comes along and takes 1/4 of them. Willow comes along and takes 2/5 of the remaining candies in the bowl, leaving 27. How many were in the bowl to start with?
 This is a classic 'work backwards' problem.
  1. If Willow took 2⁄5 of the remaining candies and that left 27 candies, then those candies were _______ of the candies after Jerry took his 1⁄4 of the original candies.

  2. _______ candies were left after Jerry took his candies.

  3. Those ______ candies are _________of the original candies, so there were originally ______ candies
2) Lisa is designing her own house. She draws a side view sketch of the stairs she wants to use to connect the downstairs with the upstairs. She notices there's a line that connects all the edges of the steps as shown in the diagram. If the coordinates giving the edge of the second step are (2ft, 3/2ft), what are the coordinates of the edge of the top step?

You must find the equation for a line given the coordinates of the second step and the fact that the line passes through the origin.





So the coordinates of the top step are (___,____)

Problem
Hint
3) At Emerald Middle School there can be at most 26 students in a class. If the ratio of boys to girls in Danny's is class is 3:2, at most how many girls can be in his class?
  1. If you divide the class into fifths (3+2) then the girls are ________ of the class.

  2. If the class has at most 26 students, then the most girls that can be in the class is _____
4) An oil slick from a leaking tanker is roughly circular in shape with radius r. The radius increases in size by 1 foot every hour. Write an expression that would compute the area of the slick 3 hours from now if the radius now is r.
  1. The formula for the current area = ______________ using r for the current radius.

  2. The area at 3 hours = _________________
5) The lines given by y = 2x + 3 and y = -x + k meet at the point (2, k-2). What is the value of k? Substitute x=2 and y=k-2 into the first equation and solve for k:




k = _____