Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 6 Number Sense

Problem
Solution

1) What is the missing number?
1. In each triangle, what is the lower left number multiplied by to get the lower right number? 3.
2. The missing number is 39
(You don't need the top numbers!)

2) 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. Take 40% off the price. That leaves $60
2. Now take 30% off that: $42

3) Emily Brown fills up her gas tank with premium gas at $2.25 a gallon. She pays $21.38. Miles Brown fills up their other car with regular gas at $2.05 a gallon. He pays $21.01. Who bought the most gas and how much more to the nearest 100th of a gallon?
l. Compute the amount Emily bought as the amount she paid divided by the price per gallon = 9.5 gallons.
2. Compute the amount Miles bought in a similar manner =
    10.25 gallons.
3. Miles bought the most gas
4. Subtract the lower amount from the upper and round to the nearest 100th of a gallon =
    0.75 gallon.

Problem
Solution
4) Carol bought 2 student tickets and 3 child tickets for a play. The student tickets cost $3.00 less than an adult ticket and the child tickets cost $4.50 less than an adult ticket. An adult ticket costs $8.75. How much money did she spend on the tickets? Work this backwards:
1. If adult tickets cost $8.75 and the child ticket cost $4.50 less,
    then a child ticket costs $4.25
2. If a student ticket costs $3.00 less than an adult,
    then a student ticket costs $5.75.
3. 2 student tickets and 3 child tickets cost
    2 x 5.75 + 3 x 4.25 = $11.50 + $12.75 = $24.25

5) Solve the riddle:
I am a 2-digit prime number
I am greater than 20 and less than 60
The sum of my digits is 10
Who am I?
The prime numbers between 20 and 60 are
    23 29 31 37 41 43 47 53 59
I am 37