Problem of the Week #19: February 25th, 2008

Grade 6:

Tommy and Sally have a box of cookies that they plan to share with three friends. Tommy and Sally discover that they number of cookies cannot be divided evenly among the five of them.
Tommy says “ If we eat one cookie the number left will make an even number of cookies for everyone.”
Sally says “ If you and I take two less cookie than our friends, then they can each have seven cookies with none left over.”
How many cookies were in the box?



Grade 7: Allowance
Miles receives a weekly allowance of $8. He can earn $5 more for each special job he completes beyond the usual chores. In twelve weeks, Miles wants to have saved enough to buy a video game player that costs $210. If he saves all of his money, how many special jobs does he need to complete to earn what he needs?



Grade 8: Shipping Cartons
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. The boxes are never mixed in a carton. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?

Grade 9: 999 Coins
Starting with a single pile of 999 coins, a person does the following in a series of steps: In step one, he splits the pile into two nonempty piles. Thereafter, at each step, he chooses a pile with 3 or more coins and splits this pile into two piles. What is the largest number of steps that is possible?
Grade 10: Multiples of Four - February 2008
How many multiples of four from 1 through 1000 do not contain any of the digits 6, 7, 8, 9, or 0?

Due to the many storm days last week I won't be posting a new set of problems until next Monday. If you have already answered your Grade Level Problem try one of the ones from a higher grade.
Have a good week.

Problem of the Week #18: February 11th 2008
Remember to submit your solutions by Friday, February 15th to tubbsjac@nbed.nb.ca

Grade 6 Problem:
McDonalds’ Restaurants sells Chicken McNuggets in boxes of 6, 9, or 20. What combination of boxes would you buy to have exactly 53 McNuggets?


Grade 7 Problem:
Goldblach’s Conjecture states that any even number greater than 4 can be written as the sum of two prime numbers (example: 8 = 5 + 3 or 7 + 1). Find four different ways to write 42 as the sum of two prime numbers.


Grade 8 Problem:
Which is more 30% of 40% of $50 or 40% of 30% of $50?

Grade 9 Problem
There are a number of coins on a table. One quarter of the coins show heads. If two of the coins are turned over, then one third of the coins show heads.
How many coins are on the table?
Does it matter if you turn over coins that show heads, coins that show tails, or one of each?

Grade 10 Problem
I used my calculator to divide two whole numbers that are both less than 100.
The solution on the calculator was: 0.739726074
What numbers did I use to get that solution?

Problem of the Week #17

Grade 6:
Fill in the blank fields by writing either 2, 5, or 10 into them so that the sum of the numbers in each column and each row is 22.
___ 2 ___ ___
___ ___ ___ 5
5 ___ ___ ___
10 ___ ___ 5

Grade 7:
Break up 60 into the sum of two numbers so that one seventh of one of the numbers is the same as one eighth of the other number.


Grade 8:
I have only $10 and $20 bills in my pocket. There are three times as many $20 bills than $10 bills. I have a total of $490. How many $20 bills do I have?


Grade 9:
A man had $10 000 to invest. He invested $4000 at 5 percent and $3500 at 4%, simple annual interest. In order to have a yearly interest income of $500, at what rate must he invest the remainder of his money?

Grade 10:
The shortest side of a right triangle is 7 cm, and its smallest angle is 15 degrees. How long is its hypotenuse?