Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 8 Algebra
Problem
Solution
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?
  1. V = P(1+r)n
  2. V = 8.5(1.03)5 = 8.5 x 1.1593 = $9.85 per hour

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 25(1+2+3) = 150 extra flies on nights 2,3 and 4.
  2. If she had not eaten those extra flies, she would have eaten 1050 - 150 = 900 flies total for the 4 nights.
  3. 900/4 = 225 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 n + 1
  2. the height is 2(n+1)
  3. The area of the 9th triangle is:
        10 x 210 / 2 = 10 x 29 = 10 x 512 = 5120 sq. units.

Problem
Solution
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 100 sq. ft./hour
  2. Sam works at a rate of 200 sq. ft./hour
  3. Let J = the rate that Jo works at
  4. So the equation is:
    1⁄6 hour x (100 sq. ft./hour + 200 sq. ft./hour + J) = 100 square feet (the whole garden)
  5. (100 sq. ft./hour + 200 sq. ft./hour + J) = 6 x 100 square feet
  6. 100 + 200 + J = 600 sq. ft./hour
  7. J = 300 sq.ft./hour
  8. Working alone, Jo can do the 100 sq. ft. garden in:
    100 sq.ft. / (300 sq. ft./hour) = 1⁄3 hour = 20 min
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.
  • Molly's Limo costs:
    1. The y-intercept is obviously $5
    2. The slope, m, is the change in cost per mile.
      Use the 0 and 2 mile points:
      m = (20 - 5)/2 = 15/2 = $7.5
    3. The equation for Molly's Limo cost is:
          Cost = $7.5 x miles + $5
    4. For a 10 mile trip it will cost:
          Cost = 7.5 x 10 + 5 = 75 + 5 = $80
  • Bob's Limo costs:
    1. (56 - 44) / (8 - 6) = $6 per mile
    2. $56 + 2 x $6 = $68
  • Bob's is cheaper by $12 for the 10 mile trip.