Problem of the Week

POW is due every Friday at the beginning of class!  Please print the answer sheet (scroll down). If you are absent you must email me your answer sheet!
Due Friday January 27
The cost of three apples and two oranges is 2 cents more than the cost of two apples
and three oranges. By how much does the cost of one apple exceed the cost of one orange?
Due Friday February 3
Suppose that n is the product of four consecutive positive integers and that n is divisible by 7.
What is the largest integer that you can guarantee will be a divisor of n?
Due Friday February 10
Pat and Chris have the same birthday. 
Pat is twice as old as Chris was when Pat was as old as Chris is now. 
If Pat is now 24 years old, how old is Chris? 
Due Friday February 17
You are working in a store that has been very careless with the stock.
Three boxes of socks are each incorrectly labeled.
The labels say red socks, green socks, and red and green socks.
How can you re-label the boxes correctly by taking only one sock out of one box? 
Due Friday February 24
What is the area of the triangle with
vertices A (3, 3), B (7, 5), and C (5, 6)?
Due Friday March 2
Find the largest integer k such that the polynomial x^2 + 8x + k can be factored
into the product of two linear polynomials, each of which has integral coefficients.
Due Friday March 9
Find all values of k for which the equations
3x + k = 2 and kx + 3 = 2 have a common solution for x.
Due Friday March 16
The equation y = x^2 + 2ax + a represents a parabola for all real values of a.  Prove that each of these parabolas passes through a common point, and determine the coordinates of that point.
Due Friday March 23
Jill pays an online service provider a fixed monthly fee plus an hourly charge for connect time.
Her December bill was $12.48.
Her January bill, for which she used twice as much connect time as in December, was $17.54.
What is the fixed monthly fee?
Due Thursday March 29 (extra credit)
A palindrome is a set of letters or numbers that reads the same forward and backward. One prime number is a factor of 2992 and all other four-digit palindromes. What prime number is it? Show how you found this!
Due Friday April 13
For all real numbers, x,  f (2x) = x^2 - x + 3.
Express f(x) in terms of x.
Due Friday April 20
You have four pieces of chain, each of which is made up of three links, all of which are closed.  If it costs 2 cents to open a link and 3 cents to close a link, how can you join all twelve links into an unbroken circle without paying
more than 15 cents?
Due Friday April 27
How must one place the integers from 1 to 15 into each of the spaces
below in such a way that no number is repeated and the sum of the numbers 
in any two consecutive spaces is a perfect square?
Due Friday May 4
A rectangle is divided into four sub-rectangles with areas 4, 7, 15, and x. Find x.

Due Friday May 11
What is the smallest positive integer by which 252 can be multiplied so
that the result is a perfect cube?
Due Friday May 18
A ball is dropped 128 feet from the roof of a building. Suppose that with
each bounce, the ball goes up exactly half its previous height. A man is
sitting at his desk on the second floor. How many times will he see the ball
if his eye level is 15 feet above the ground?
Due Friday May 25
How many distinguishable rearrangements of the letters in the word CONTEST
start with the two vowels?
Due Wed, May 30 (extra credit!)
Find the points at which the line 3x+y=5 intersects the circle x^2+y^2-2x-3=0.
Julie McGee,
Aug 24, 2011, 7:46 AM