Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 5 Algebra
Problem
Solution
1) Joni is watching her baby sister stack blocks and has discovered that there's an actual pattern! How many blocks would the 7th tower have?
 This is an arithmetic sequence.
Method 1: Extend this to the 7th stack
Write down the number of blocks in each stack, like this:
1 ... 4 ... 7 ... 10 ...
Determine what is added to each term to get the next: =
3 blocks.
Extend this list to the 7th stack.
1 ... 4 ... 7 ... 10 ...13 ... 16 ... 19
The 7th stack has 19 blocks.

Method 2: Use the arithmetic sequence formula:
    An = A1 + D (n - 1), where:
    An = the nth term (the one you're looking for)
    A1 = the first term and D is the delta between each term.
    An = 1 + 3(7 - 1)
    An = 1 + 18 = 19 blocks
2) The Math Club has a Math Olympiad clock made for their coach where the numbers on the clock are replaced with the letters MATH OLYMPIAD. The M is at 12, A at 1, all the way around ending with D at 11. It is now 2 o'clock with the hour hand pointing to the T. One hundred hours later, which letter will the hour hand point to? 1. Divide 100 by 12 to get the total number of 12-hour periods. = 8
2. The remainder will be the number of hours past a full 12-hour period. Remainder = 4
3. Add 4 because you started at 2 and then find the corresponding letter = 7th letter = "Y".

Problem
Solution
3) Swiper, Dora, and Bob collect Pokemon cards. Swiper has 15 Pokemon cards. Dora has 3/5 more cards than Swiper. Bob has 2/3 more cards than Dora. How many cards does Bob have? 1. Swiper has 15 cards.
2. Dora has 3/5 more cards than Swiper which is 15 X (5/3) = 24 cards.
3. Bob has 2/3 more cards than Dora which is 24 X (3/2) = 40 cards.

4) Lena is keeping track of time as she walks a trail in the park. This is the chart below she created with her data when she got home. What time was it when she passed the 2 3⁄4 mile marker?
1. Using the 1-mile marker, determine her walk rate:
    (1:21 - 1:05) = 16 minutes per mile.
2. Multiply by 2 3/4 and add to her start time.
    Time = 16 x 11/4 = 44 minutes.
    1:05 + 44 minutes = 1:49 o'clock.
5) I'm a mystery number. If you multiply me by 3 and then add 4 the result is the same number if you multiply me by 4 and then add 3. What number is the result and what number am I? An algebra problem! You have to write an equation. Use X for your mystery number.
1. The left side of the equation is "multiply me by 3 and then add 4".
    Using X this is 3X + 4
2. the right side of the equation is "multiply me by 4 and then add 3".
    Using X, this is 4X + 3
3. Set these two expressions equal to each other and solve.
    3X + 4 = 4X + 3
    X = 1