Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 5 Algebra

Problem
Hint
1) A girl walks a straight path from her home to go play in the park. When she is 1/3 of the way along, she realizes she has dropped her mittens. She walks back 120 meters to retrieve them. She is now 420 meters from home. How far is she from the park? 1. The distance she walks back to get her mittens + the distance from home after she retrieves her mittens is 1/3 of the distance to the park.
    1/3 of the distance to the park is ____ + ____ = _____ meters.
2. So the distance from home to the park is 3 X ____ = _____ meters.
2. Since she was 420 meters from home when she picked up her mittens she was ____ - 420 = _____ meters from the park

2) Find the area of this rectangle. Its perimeter is 20 feet. Round to the nearest hundredth.
1. The equation for the perimeter is:

    2(3X - 4) + 2X = 20 ft.

2. Solve this for X = _____ ft.
3. Compute the area given this measurement.
Area = _____ sq. ft.

3) Every week, Amy helps her neighbor clean their home and does extra chores around their house. She is paid a fixed amount for the cleaning and an additional hourly amount for the extra chores. Based on the table below, how much is the hourly amount for the extra chores?

Hours of extra chores3712
Total amount earned  $58  $102  $157 
The only data points you need are the first 2.
1. The extra amount she earned in week #2 is ____ - ____ = _____.
2. The extra hours she worked chores in the second week over the first week is ____ - ____ = _____ hours.
3. Divide the first amount by the difference in hours to get the hourly rate = $_____ /hour.
4. Check it using the 3rd week.

Problem
Hint
4) When a one-digit number is multiplied by 8, it increases by 42. What is the one-digit number? Use X for the one-digit number.
1. Expression for "one-digit number is multiplied by 8" = ______.
2. The expression for "it increases by 42" = ___________.
3. Set these 2 expressions equal to each other and solve.
X = ____
5) Louis is stacking textbooks and starts forming a pattern. If the pattern below repeats, how many books will there be in the 7th stack?
This is an arithmetic sequence.
Find the number added at each stack: = _____
Method 1: Write out the total number of textbooks for each stack:

You should see a pattern here. Extend the sequence to 7 elements and compute the number of textbooks in it = _____.

Method 2: Use the equation for finding the nth element of an arithmetic sequence:
    an = a1 + d (n-1) where:
    an = the nth element (the one you're looking for)
    a1 = the first element and
    d = the number of textbooks added to each stack
    a7 = _____