Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 7 Number Sense
Problem
Hint
1) Grandpa tells Nelli he has an investment in a fund that has a history of increasing in values by 6.2% every year. He has $32,000 invested in that fund. He asks her to compute how much the fund will earn him over five years if he makes no changes to his investment. Express your answer to the nearest cent. Careful! They are asking for the amount he earns, not the total value of his investment after 5 years!
The formula for compound interest is:
    A = P (1 + r) t where:
    P is the principal
    r is the interest rate (in decimal)
    t is the number of time periods (in our case, years)
  1. Compute the value of his investment after 5 years:


        P = ______
  2. Subtract the original investment value to get how much he earned:
2) Ben wants to make a lot of crepes. He has 3 cups of milk left and 1 and 1/2 cup of flour. He has plenty of eggs and everything else he needs. The recipe calls for 3/4 cups milk and 3/8 cup flour and yields 6 crepes. What is the maximum number of crepes he can make with the ingredients he has?
  1. Compute the number of recipes he can make with his milk


        n = ______
  2. Compute the number of recipes he can make with his flour


        n = _____
  3. So he can make ____ crepes.

Problem
Hint

3) The numbers 1 - 32 can be represented with a set of five lights using the binary system. An on light is recorded with a 1, an off light is recorded with a 0. With the pattern given in the table, how would the number 23 be represented in 1's and 0's?
 This is the binary number system. In this system, each binary digit (bit) is a power of 2, from right to left, so the 32 this problem talks about with 5 'lights' is 25 = 32, the left-most row of this table. All you have to do is make up the number 23 with these powers of 2!





  23 = ___ ___ ___ ___ ___
4) The volleyball coach recorded the ratios of successful serves for the four best players as shown in the table. Based on the current records, if they were all to serve 20 times, what would be the difference in number of successes between the top record and the second best record? Round to whole number of serves.
  1. First, turn all the fractions into percents (or decimals) to make comparisons easier:



  2. Find the top 2 servers, take the difference between their successful percentages and multiply by 20:




        Difference = _____ serves

5) a) Which expression is bigger:
    (-1/2) + (1/3) + (-1/4) or
    (-1/2)(1/3)(-1/4)?
b) How much bigger is it?
Express your answer as a reduced fraction.
  1. First expression: convert them all to a common denominator and add =


  2. Second expression: multiply it out (be careful with the signs!)


    = ______    
  3. Determine which expression is larger (not just in absolute magnitude) and subtract the other expression's value from it:


        The larger expression is larger by _________