Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 8 Number Sense
Problem
Hint
1) At Bob's school the price of school t-shirts goes up by 10% rounded to the nearest cent each year. This year the price of the t-shirt is $10. What will the price be 4 years later?

 This is a compound interest problem:
V = P(1 + r)n where:
P is the starting principal,
r is the interest rate in decimal
n is the number of periods.



Value after 4 years = _________
2)In Kyle's English class 4 students have green eyes. 5/8 of the students have brown eyes and 1/4 of the students have blue eyes. There are no other eye colors. How many students are in his class?

  1. The fraction of the students that have either blue or brown eyes is:


    _____________
  2. Therefore, the 4 students with green eyes are __________ of the students, so there are _____ students in his class.
3) On a number line, what fraction is halfway between

    1⁄3 - -3⁄4 and -3⁄8 - 5⁄6?

Add the two expressions together and divide by 2. Be careful! Lots of common denominator arithmetic!





= _________

Problem
Hint
4) Liz was playing with a pile of pennies. She noticed when she stacked them in piles of three there was 1 left over. When she stacked them in piles of five there were 2 left over. When she stacked them in piles of seven there were 3 left over. What is the smallest number of pennies she could have? Start with stacks of 7 and compute the remainders of stacking in 5s and 3s. Stop when you get 2 left over in stacks of 5 and 1 left over in stacks of 3:
# stacks
of 7
(N)		 Total
pennies

(7N + 3)		 # stacks of 5 + remainder # stacks of 3 + remainder
217
3
4
5
6
7
8

Liz has ____ pennies.
5) How many perfect square numbers will there be in the first century of the third millennium, so between 2000 and 2100? List them. Take the square roots of 2000 and 2100. Take it from there.