Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 8 Algebra
Problem
Hint
1) Kyle is hired in 2013 at a company where he earns $8.50 an hour. The company awards an annual pay raise of 3% to the nearest penny to all of its employees. What will Kyle's hourly earnings be in 5 years if he continues working for this company in the same position? The formula for compound interest current value is:
V = P(1+r)n
Where P is the starting principal
r is the rate specified as a decimal
n is the number of periods.



V = _____

2) A bat ate a total of 1050 flies on four consecutive nights. Each night she ate 25 more than the night before. How many flies did she eat the first night?
  1. The bat ate a total of _____ extra flies on nights 2,3 and 4.
  2. If she had not eaten those extra flies, she would have eaten _____ flies total for the 4 nights.
  3. The bat ate ____ flies the first night
3) Consider the sequence of right triangles shown. If the patterns in the base and height lengths continue, what is the area of the 9th triangle in the sequence in square units?
 Use n for the triangle number.
  1. The base of the triangles is __________ (in terms of n)

  2. the height is ______

  3. The area of the 9th triangle is:





    _____ sq. units

Problem
Hint
4) The Green's family garden needs to be weeded. Chris can weed the garden in 1 hour. Sam can weed the garden in 1/2 hour. When Jo helps them, they can weed the garden in 10 minutes, all working together. How long would it take Jo to weed the garden working alone? Give your answer to the nearest minute. Assume some easy garden area to compute with, like 100 sq. ft.
  1. Chris works at a rate of _____ sq. ft./hour

  2. Sam works at a rate of _____ sq. ft./hour

  3. Let J = the rate that Jo works at
  4. So the equation is the time (in fraction of an hour) times the combined rates of the 3 people and set that equal to the area of the garden.





  5. Working alone, Jo can do the 100 sq. ft. garden in:
    _____ minutes
5) Molly's Airport Limo Service advertises her rates with the graphic shown, while Bob's Limousine Service uses the table that represents linear data. My sister and her fiance want the cheaper limo ride on their wedding day for the 10 mile trip to the airport. Which one is cheaper and what is the positive difference between the cost of the 10 mile trip with each service?

 You must find the equation of the line in y = m x + b form where m is the slope and b is the y-intercept.




For Molly's limo, a 10 mile trip it will cost: ______





For Bob's limo, a 10 mile trip it will cost: ______

_____ is cheaper by _____