Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 6 Algebra
Problem
Hint
1) Parmveer has a bag with 54 coins. Altogether the coins are worth $4.75. He only has nickels and dimes in the bag. How many dimes are in the bag?
Method 1: guess-and-check. Just make sure your guesses for the number of coins is 54. Here is the table:
# nickels#dimesTotal
2628$4.10
   
   
   
   
   
 Method 2: Use 2 equations.
Use N for the number of nickels and
    D for the number of dimes.
1. The equation for the number of coins:
    N + D = 54
2. The equation for the sum of the coins:
    5N + 10D = 475
3. Write an expression for N using the first equation and then substitute it in the second equation and solve.
    D = _____
2) Evaluate:
    8x2 - (4x - 17) if 4x - 11 = 3		 1. Rewrite the second expression as
    x =

2. Substitute it in the first equation and solve for x:
   
3) Shalem started with a certain amount of money. Every day he spends the same amount. After the 4th day he has $117 left. After the 36th day he has $13 left.
    a. How much money did he start with?
    b. How much does he spend each day?		 1. Subtract the amount he had after the 36th day from the amount he had after the 4th day and divide by the number of days between them = $_____/day
2. Add 4 times the daily amount to his 4th day total get the amount he started with = $_____

4) In Josie's class there are 28 students. 13 have been to Oregon, 11 have been to Idaho, and 3 have been to both. How many students have not been to either Oregon or Idaho? Method 1: Use a Venn diagram
1. Draw 2 overlapping circles for Oregon and Idaho.
2. Draw the numbers in the diagram and then add the 3 components = ____ students have been to Oregon, Idaho or both.
3. Subtract this from 28 = _______
Method 2: Use logic:
1. If 13 students have been to Oregon and 3 of those also have been to Idaho, then ___ have been to Oregon only.
2. If 11 students have been to Idaho and 3 of those also have been to Oregon, then ___ have been to Idaho only.
3. Add these two to the number that have been to both =
    _____ students
4. Subtract this from the total: _____
5) I'm thinking of a positive number. If I square it and then subtract 65, I get the same answer as when I multiply my number by 8. What is my number? Use x for your number.
1. Write an expression for "square it and subtract 65" = ______
2. Write an expression for "multiply my number by 8" = ____
3. Set these equal to each other and solve. x = _____