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

Problem of the Week #21: March 17th to 21st 2008


Grade 6:
Using the pattern in the following table
find the value of the missing number in the
bottom right corner. 4 9 11
6 8 12
13 16 27
19 26 43
23 7 28
31 47 ?




Grade 7:
Continue the following pattern to find the next 5 terms

17, 8, 25, 7, 32, 5, 37, 10, 47, 11, 58, 13, ___, ____, ____, ____, _____ .

Grade 8:
Find the values of a and b if both the median and the mean of the number set is equal to 8.
{ a, b, 10, 7, 11}

Grade 9: Suppose that 7! is written as a product abcd, where a, b, c, and d are positive integers such that each of a, b, c, and d has the same number of positive integral divisors. (As an example, 6 has four positive integral divisors: 1, 2, 3, and 6.) What is the value of a + b + c + d ?
Grade 10: Can you make the following problem a true statement by repositioning one and only one digit in the equation? You cannot add or subtract any mathematical symbols or move the – or the = signs. Equation: 26 – 63 = 1

Problem of the Week #20: March 10th – March 14th, 2008

Grade 6:
A student had twenty dollars. He went to the movies. He paid $ 8.00 for admission, $4.00 for popcorn and $2.50 for a soda and $1.50 for candy. When he looks at his change he has 8 coins. What coins does he have and how many of each does he have?

Grade 7:
The difference of two perfect square three digits numbers is a perfect square number. What are the two numbers and what is the difference?

Grade 8:
A three digit number ABC is divisible by 7 and the same three digits when arranged in the order CBA is also divisible by 7. Find one possible combination for ABC.

Grade 9:
A right triangle has sides measuring 20 cm, 15 cm and 25 cm. Find the shortest altitude for this triangle.

Grade 10:
I am thinking of a three digit number. If I reverse the digits so that the hundreds digit and the ones digit are reversed I get another three digit number. If a multiple the original number by the reversed number the product is 65 125. What is the smaller three digit number?