Problem of the Week #27: Posted May 20, 2008

Grade 6
Six monkey statues are arranged in a row from left to right. Each monkey is a reflection of the one sitting beside it on its left. If the first monkey has its right paw raised, what paw does the last monkey have raised?

Grade 7
If my garden is a rectangle in shape and has an area of 40 square metres what is the least amount of fence I need to go around the garden?

Grade 8
A ladder is leaned against a vertical wall such that the slope of the ladder is 9/4.
The ladder reaches a point on the wall that is 13.7 metres from the ground. If the ground is level, what is the length of the ladder?

Grade 9
What is the shape of the graph of all the solutions to the equation

Grade 10
List all the Pythagorean triples by creating a formula to determine such.

Problem of the Week #26: May 5th, 2008 – May 9th , 2008

Grade 6
There are 12 eggs in a carton, and 8 cartons in a crate. Twenty crates of eggs were delivered to the SuperStore. How many eggs were in the shipment?

Grade 7
A cat had a litter of kittens. One quarter of the kittens are female. One third of the male kittens and one third of the female kittens are black. If there are four black kittens all together, how many kittens were in the litter?

Grade 8
A 60 passenger bus begins its run at the first stop by picking up half its capacity. At the next stop three people get off, but five people get on. At the next stop half the people get off but twelve more get on. At the next stop one quarter of the passengers get off the bus, but three people get on. What lowest term fraction expresses the load of the bus? ( number of passengers compared to capacity).

Grade 9
You are standing in line to see a movie. You notice that there are five more people ahead of you in the line than there are behind you. Four times as many people are in the line as the number who are behind you. How many people are ahead of you in the line?

Grade 10
Find two whole number factors of one billion that do not contain any zeros as a digit. In other words, what two whole numbers that contain no zeros can be multiplied to get a product of 1 000 000 000.

Problem of the week #25: April 21 – April 25, 2008

Grade 6
How many numbers between 20 and 40 have exactly four factors?

Grade 7
I used my calculator to divide two whole numbers. The answer on the calculator is 3.125 but I don’t remember what numbers I divided. Do remember that they were both less than they were both less than 50. Can you find what numbers I divided?

Grade 8
I used my calculator to divide two whole number and got a solution of 3.571428….
I don’t remember the numbers but I know they were both less than 30. What numbers did I divide?

Grade 9

I used my calculator to divide two whole numbers and got a solution of 1.846153…..
Both numbers were less than fifty. Can you find two division statements that solve the problem?

Grade 10

I used my calculator to divide two whole numbers less under 100 and found the answer to be 0.73997270274. Can you find what the numbers were?

Problem of the Week #24: April 14th , 2008

Grade 6
Two grade 6 students started a special club. They agreed to each get a new member to join their club every month. Each new member would also find a new member by the end their first month and every month after that. If the club started on the first of September how many members will it have by the end of June?

Grade 7
Joe does a lot of travel by plane. Yesterday he departed St. John’s Newfoundland at 10:15 am (Newfoundland Time) and flew to Toronto. His flight landed in Toronto at 1:15 pm (Eastern Time). How long was the flying time between departure and landing?

Grade 8
A taxi trip in the city of Ottawa is a combination of a base charge plus a distance charge.
A1 Taxi charges a base rate of $3.00 plus $1.50 for every kilometer traveled. B-Sure Taxi charges a base rate of $5.00 plus $1.00 per kilometer. If the trip from the hotel to the airport is 20 km which company is the best deal and how much do you save?

Grade 9
The legs of a right triangle measure x + 3 and x - 2 respectively. What is the area of the square on the hypotenuse?
If the area of the hypotenuse square is 53, what is the value of x?

Grade 10
A single elimination tennis tournament has 1998 participants. In every round players winning the game advance to the next round, the losers go home. A player with no opponent automatically advances to the next round. How many games is needed to find the best player?

Problem of the Week # 23: April 7th 2008

Grade 6:
Jill went to the school store and bought the following items;
4 pencils for $0.23 each, 2 pens for $0.59 each, one notebook for $0.90 and a binder for $2.50. There was not tax on these items. Jill paid with a $10 bill. How much change did she get back?

Grade 7:

Find five Prime numbers that add to make 43 for a total. Arrange them in order from smallest to largest and give the Median of the five numbers.

Grad 8:
Determine the smallest positive integer that consists of different digits, all of which are even, that is also a multiple of 9?

Grade 9:
If the mean of twenty different positive integers is 20, what would be the greatest possible value of any one of these twenty numbers?

Grade 10:
A Mathematician noticed that the numbers 992 and 578 have a special property: the sum of the digits of each number is equal to 20. ( 9 + 9 + 2 = 20 and 5 + 7 + 8 = 20)
How many other three digit numbers have this property?

Problem of the Week #22: March 31, 2008

Grade 6:
Find the next three numbers that fit the following pattern
3,7,10,17,27,44, 71, ___, ___, ___

Grade 7:
Find the next three numbers that fit the following pattern
2, 8, 4, 10, 5, 11, 5.5, ___, ___, ____

Grade 8:
Jill paid $ 5.55 for one notepad and 7 pencils. Anne paid $ 12.28 for three of the same notepad and two of the same pencils. How much does a notepad cost?

Grade 9:
Jane cashed her birthday cheque and decided to use the money for good causes. She gave 10% of her money to Safe Grad. From what she had left she gave one third to the Food Bank and gave the $72.00 that was left to the SPCA. How much did Jane give to Safe Grad?

Grade 10:
What is the smallest three-digit number you can obtain from the product of two or more distinct (not repeated) prime numbers?

Because of the storm day on March 20th and the Good Friday and Easter Monday School Holidays I am taking the week off to give teachers and students a chance to catch up and submit their solutions to last week's problems.

Here is a problem if you are desparate for a challenge.

There are 24 students in Mr. Smith's Physical Education class. Each student is wearing either shorts or running shoes or both shorts and running shoes. If the following facts are true:
16 students are wearing shorts
20 students are wearing running shoes
How many students are wearing both shorts and running shoes?
Find the answer and Tell me how you solved this problem.
Submit solutions to tubbsjac@nbed.nb.ca