Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 7 Algebra

Problem

1) In which equation does X have the greater value?
    a) X + 212 = 514 or
    b) X - 1.7 = 2.05 or
    c) 6 / X = 2.1

2) Jim has a balanced scale and several metallic coins. He finds that:
    2 gold coins = 3 silver coins and 1 copper coin
    2 silver coins = 1 copper coin and 1 bronze coin
    3 copper coins = 2 bronze coins

How many bronze coins will it take to balance 12 gold coins?

3) Marcia is saving up to buy a book collection by her favorite author. The book collection costs $65. Marcia receives a $10 allowance every week, and she spends $8 every other week to see a movie with her friends. If she doesn't attend a movie on the week that she begins saving for the book collection, how many weeks will it be before she has saved enough to afford it?

4) Mikael is training for a fun run by jogging a five-mile loop around a lake every morning. After the first mile, he starts to slow his pace at a steadily decreasing rate. He records the following regarding his progress and time:

What time will he finish his jog?

5) You are mailing a large envelope that will require $2.30 in postage. Using only stamps valued at 15 and 25 cents, how many ways can you cover the exact postage?