Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 6 Algebra
Problem
Hint
1) Terri wants to buy some gum and comic books for a road trip. She is going to buy twice as many comic books as gum. Each package of gum costs $1.10 and each comic book costs $2.75. Terri lives in Oregon so there is no sales tax. What is the maximum number of comic books she can buy if she has $25 to spend? Let C = the number of comic books.
1. Then C x $2.75 is the amount spent on comic books
2. C/2 x $1.10 is the amount spent on gum
3. Write an equation that sums these two and makes them equal to the amount she has to spend and then solve for C.
4. Now, here's the tricky part! If this is an odd number, you must subtract 1 because half of an odd number of comic books is not a whole number of packs of gum!
5.     C = _____

2) Gerald buys apples and broccoli for his restaurant in whole numbers of pounds. Apples cost $2.33 per pound and broccoli cost $2.10 per pound. Gerald pays with a twenty dollar bill. If he gets $8.04 back, how many pounds of broccoli did he get?		 This is a guess-and-check problem.
The amount Gerald spent was $20 - the amount he got back = _____.
Note: If you divide this amount by $2.20 (roughly the average cost of both a pound of apples and broccoli) you get the approximate number of pounds of both.
Use this table:
Guess ## pounds
broccoli		# pounds
apples		    Total   
cost
153$17.49
    
    
    
    
    

Problem
Hint
3) Figures #1, 2 and 3 of a sequence of growing dots figures is shown. If the sequence continues in the growing pattern how many dots would be in figure #9?
 1. The answer involves exponents.. The exponents are used on the figure numbers.
2. The next 3 figures (#4, 5 and 6) contain
    17, 26 and 37 dots.
3. Figure #9 contains ____ dots.

4) Sidewalk Pizza Pockets sells pizza pockets. The table shows the prices for 3 pizza pockets, 6 pockets and 12 pockets. Based on the table how much should one pizza pocket cost to the nearest cent?
1. Divide the price for 3 pockets by 3 to get the price per pocket = _____.
2. Round to the nearest cent = _____.
5) Nicky says "Think of a number. Add 7 to it and multiply the result by 4. Then subtract 4, take a quarter of the result and subtract your number. I know the answer." Will Nicky always be right? If so, what is the answer? If not, show with examples why Nicky can't always know the answer. Use X for Nicky's number.
1. Write out the expression (it involves a lot of parentheses) and reduce it.
2. The result is _____