Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 7 Number Sense
Problem
Solution
1) Right after Christmas a store put all of its winter coats on sale for 40% off. One rack had a sign saying, "Take an additional 30% off". Terri picks out a blue coat from this "30% off" rack. If the coat had an original price of $100.00, what will the coat now cost Terri? (Do not include tax.)
  1. A discount of 40% is a multiply of the principal (P) by .6
  2. (100 x .6)x .7 = 100 x .42 = $42
2) What is the missing number?
  1. In the first triangle the lower left number is multiplied by 3 to get the lower right number
  2. In the second triangle the lower left number is multiplied by 4 to the lower right number.
  3. In the third triangle the lower left number is multiplied by 5 to get the lower right number = 50

3) The Monday after Thanksgiving is now called "Cyber Monday" and is the busiest on-line shopping day of the year. On Cyber Monday 2004, credit card users for one company spent 4/5 the amount of money they spent on Cyber Monday in 2005 How much more money, expressed as a percentage, was spent in 2005 compared to 2004? 		For convenience, assume that the credit card users spent $100 in 2005.
  1. The they spent 4⁄5 x $100 = $80 in 2004.
  2. They spent $100 - $80 = $20 more in 2005.
  3. This is 20/80 = 25% more.

Problem
Solution
4) The odometer on a car reads 42322 miles. In the next 200 miles how often will the odometer show a number in which exactly three of the digits are the same?
  1. In 200 miles the odometer will read 42522 miles
  2. The numbers are between 42322 and 42522
  3. Here are the numbers
    • 42333
    • 42344
    • 42422
    • 424x4 where x is not 2 (9 of these)
    • 4244x where x is not 2 (9 of these)
    • 42522
There are 22 numbers
5) A pound of hamburger is 30% beef, 30% cereal, 20% water and 20% ingredients untouched by human hands. If one pound equals 16 ounces, determine the water content in ounces of a Quarter Pounder.
  1. 1⁄4 of 16 = 4 ounces
  2. 4 ounces x .2 = .8 ounce