Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Algebra

Problem
Hint
1) Tina and Jeff each bike 3 miles to school. Jeff bikes a steady 1/4 of a mile per minute. Tina bikes a steady 1/6 of a mile per minute. When Jeff arrives at school, how far does Tina still have left to bike?
  1. If Jeff bikes at 1/4 mile per minute for 3 miles, how long does it take him to bike a mile? ___ minutes.
  2. Then for 3 miles it takes him ___ minutes.
  3. In that amount of time, at 1/6 mile per minute, how far does Tina bike? ______________ miles
  4. How much distance is left for Tina to ride? ___ miles
2) The boy scouts are building bird houses. Michael buys screws and nails for the project. Screws go for 65 cents per pound and the nails go for 30 cents per pound. Michael bought 3 pounds of screws and he spent a total of $4.05. How many pounds of nails did he buy?
  1. If Michael bought 3 pounds of screws, how much did he pay for them? _____
  2. If he spent a total of $4.05 for both the screws and the nails, how much did he pay for the nails? _______
  3. At 30 cents per pound, how many pounds of nails did he buy? _____

Problem
Hint
3) The colored stripes pattern Red, Blue, Orange, Green, Yellow repeats on wall paper. What will be the color of the 32nd stripe? There are 5 stripes and they repeat every 5 stripes, so determine how many repeats of the 5-stripe pattern there are and then the remainder will be the number of the stripe that is #32.
4) Tran loves jellybeans. Every day he eats one more jellybean than the previous day. If Tran ate 15 jellybeans on Saturday, how many total jellybeans did he eat that week if his week began on Monday and ended Saturday?
Method 1: Make a table
Make a table that looks like this:
Day# jellybeans
Saturday15
Friday
Thursday
Wednesday
Tuesday
Monday
Total
Method 2: Use logic
1. If Tran ate 15 jellybeans every day he would eat ____ beans for the week.
2. If he ate 15 on Saturday, he must have eaten ___ on Friday, and then ____ on Thursday.
3. Add up all the beans he did not eat = ____
4. Subtract this from the top number. He ate ____ total beans.
5) Sosna is moving. She can carry 16 books at once in her arms to the car. She can also carry 26 DVDs in one load. She doesn't mix books and DVDs to keep things organized. Sosna made 7 trips to the car with arms fully loaded and carried a total of 142 objects. How many DVDs did she carry to the car? This is a Guess-and-Check problem!
Make a table that looks like this:
Make sure the number of trips is 7.
Guess # #trips to the car#book trips# DVD tripsTotal number of objects
17343 x 16 +
4 x 26 = 152
27
37
47
57