Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 7 Algebra
Problem
Hint
1) Rudi and Ria go to the gym to do some weight lifting. Rudi goes first on the bench press, loading on three identical weights on each end of the bar. Ria can't lift as much and replaces each of the weights with weights that are 15 lbs lighter. If she is pressing 94 lbs total, what was Rudi pressing?
  1. One of the 6 of Rita's weights weighs _____ pounds.
  2. Add 15 pounds to get Rudi's individual weights = _____ pounds each.
  3. Multiply by 6 to get Rudi's total weight = _____ pounds
2) Megan wants to buy some bracelets and necklaces. Each bracelet is $8 and each necklace is $12. She buys a total of 12 items. How many of each did she buy if she has $100 to spend? Disregard sales tax. This is 2 equations with 2 unknowns.
Let N = the number of necklaces and
B the number of bracelets.
  1. Write out the 2 equations:


  2. Turn the first equation around to solve for N:


  3. Substitute this expression for N in the second equation and solve for B



    = _____
  4. With this value for B, solve for N = ____
3) I'm a mystery number. If you multiply me by 4 and then add 3 the result is the same number if you first add 4 to me and then multiply the result by 3. What number am I?
 Using X for the mystery number, the equation is:




Solve this for X = _____

Problem
Hint
4) Consider the pattern of arrangements of squares. The perimeter of the 1st arrangement is 4 units. What is the perimeter of the 10th arrangement of squares?
  1. Write out the sequence of perimeters:
        ___   ___   ___
  2. Each perimeter adds ___ units to the previous one. This is a arithmetic sequence
  3. The equation for the nth term of an arithmetic sequence is:
        An = A1 + d (n-1) where:
        n = the term desired
        d is the number added to each term


  4. Solve for A10 = ______
5) 14 monkeys are bouncing on the bed and one falls off every 2 minutes. Create a graph with appropriate scale that expresses this problem on the coordinate system provided on the answer sheet. The graph should show the x and y intercepts. What is a linear equation that passes through the integer points on the graph?
 Plot the points on the graph to the left.
  1. 14 monkeys are on the bed, so ____ is the y-intercept
  2. Every 2 minutes one falls off, so the slope is
    _______
  3. The equation of a line is
        y = mx + b
  4. Using this form, write out the equation of the line: