Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Algebra
Problem
Solution
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. Jeff bikes 4 minutes per mile
2. So for 3 miles he takes 4X3 = 12 minutes.
3. Tina takes 6 minutes per mile, so for 12 minutes she goes 12/6 = 2 miles.
4. Tina must go 1 more mile.
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? 3 x 65 cents = $1.95
  2. If he spent a total of $4.05 for both the screws and the nails, how much did he pay for the nails? $4.05 - $1.95 = $2.10
  3. At 30 cents per pound, how many pounds of nails did he buy?
    $2.10 / $.30 = 7 pounds

Problem
Solution
3) The colored stripes pattern Red, Blue, Orange, Green, Yellow repeats on wall paper. What will be the color of the 32nd stripe? After every 5 stripes the pattern repeats, so the red strips are stripes #1,#6, #11, #16, #21, #26 and #31. Therefore after the 30th stripe the pattern starts to repeat and the second stripe, the BLUE stripe will be #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
Day# jellybeans
Saturday15
Friday14
Thursday13
Wednesday12
Tuesday11
Monday10
TotalAnswer: 75
 Method 2: Use logic
  1. If Tran ate 15 jellybeans every day he would eat 15 x 6 = 90 beans for the week.
  2. If he ate 15 on Saturday, he must have eaten 14 on Friday, and then 13 on Thursday.
  3. Add up all the beans he did not eat =
        1+2+3+4+5 = 15
  4. Subtract this from the top number.
        He ate 90 - 15 = 75 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? 4 book trips @16 books per trip = 64 books
3 DVD trips @26 DVDs per trip = 78 DVDs.
64 + 78 = 142 objects.