Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 7 Algebra
Problem
Solution
1) Billy wants to purchase a new bike which costs $185. Billy mows lawns in his neighborhood to earn money. For each lawn Billy mows he makes $10. After every 3 lawns he mows, Billy must refill his mower's gas tank. It costs $8.50 to refill the tank. How many whole lawns will Billy have to mow to make enough money to buy the new bike?
  1. For every 3 lawns, Billy's profit is _____
  2. Dividing the price of his bike by this gives ____ 3-lawn cycles.
  3. At the end of these ____ 3-lawn cycles he has made a profit of ______ leaving him needing ____ to get his bike.
  4. To make that last ____ he needs to mow ___ more whole lawns, for a total of _____ lawns.
2) Consider the sequence of triangles shown. If the patterns in the side lengths continue, what is the area of the 5th triangle in the sequence in square units?
 Call the base of the triangle b and it's height h and the figure number n (1, 2 and 3).

In terms of n, the bases, b, are _____ in length.
  1. Figure out the relationship of the height, h, to the base (it involves exponents)

    h = ______________

  2. The area of the 5th triangle = ______________

Problem
Solution
3) Marie lives 5 miles from school and bikes at an easy rate of 6 miles per hour. Her sister Kate takes the same route but is a bike racer. She rides at a rate of 25 miles per hour. If they arrive at school at the same time, how many minutes earlier than Kate does Marie need to leave?
  1. Divide Marie's distance by her rate to get her time = _______minutes
  2. Divide Kate's distance by her rate to get her time = _____ minutes.
  3. Marie leaves _____ minutes earlier.

4) Consider the sequence of figures made up of little squares shown. Divide the total number of little squares in Figure 10 by 11. What is that quotient?
 Careful! Tricky wording! They are asking for the number of squares in the 10th figure divided by the number 11, not the number of squares in the 11th figure!
Use n for the figure number.
  1. The number of squares in the figures are
        ___, ___ and _____
    This is an arithmetic sequence where each figure adds ____ squares.
  2. The formula for the nth figure is
    An = A1 + d (n - 1)
  3. Putting in our values:
    A10 = _____
  4. Divide this by 11 to get the quotient: _____
5) Molly's Limo service provides the graphic below to display its airport service prices. I live 20 miles from the airport. What will it cost me if I use this 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.
  1. The y-intercept is _____
  2. The slope, m, is the change in cost per mile.
    Use the 0 and 2 mile points:

    m = _____
  3. The equation for Molly's Limo cost is:

        Cost = ___________________
  4. For a 20 mile trip it will cost:
        Cost = ______