# Algebra 2 Problems of the Week

 POW Answer Sheet ```Due September 1-3 Sandra 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 September 6-10 The measures of the four interior angles of a quadrilateral are x, 2x, x + 20, and x + 40 degrees. How many degrees are in the measure of the smallest interior angle of the quadrilateral? Due September 13-17 The rectangle has area 180 and consists of nine congruent sub-rectangles. Find its perimeter. Due September 20-24 A store had a sale on eggs, selling thirteen eggs for the usual price of a dozen eggs. As a result, the price of eggs was reduced by 4 cents a dozen. What was the original price for a dozen eggs? Due September 27-Oct 1 Positive integers B and C satisfy B(B - C) = 23. What is the value of C? Due October 4-8 If x, y, and z are positive, with xy = 24, xz = 48, and yz = 72, then compute x + y + z. Due October 12-15 A military band was marching in formation. At first, the marchers formed a perfect square with an equal number of columns and rows, but then they changed formation and became a rectangle with five more columns than before. How many musicians were in the band? Due October 18-22 Three consecutive positive prime numbers have a sum that is a multiple of 7. What is the least possible sum? Due October 25- 29 Using the numbers 3, 3, 7, and 7, along with any of the symbols +, -, x , ÷, and parentheses, obtain a total of 24. Due November 1-5 You have twelve coins, one of which is counterfeit and weighs less than the legal coins. How can you use a simple balance three times to determine which coin is counterfeit? Due November 8-12 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 November 15-19 How many three-digit numbers consist only of odd digits? Due November 22-23 A die, with the numbers 1, 2, 3, 4, 6, and 8 on its six faces, is rolled. After this roll, if an odd number appears on the top face, all odd numbers on the die are doubled. If an even number appears on the top face, all the even numbers are halved. If the given die changes in this way, what is the probability that a 2 will appear on the second roll of the die? Due November 29 - Dec 3 You and a friend are playing anti-ticktacktoe, where three in a row loses. You are O. If you want to win, what must your next move be? Due December 6-10 The vertex of the parabola y = (x - b)^2 + b + h has coordinates (2, 5). What is the value of h? Due December 13-17 One whole candle can be made from four candle "stubs" left in the candleholder after the candles burn down. If each candle burns down to a stub after one night and if you have purchased sixteen candles, then for how many nights will you have candles to burn? Due December 20-22 One day in the past, the following statements were true. Today Jennie was 18 years old. The day before yesterday, she was 17. Next year, she will turn 20. She was not born on 29 February, and her age is given in human years. She does not age at a different pace from anyone else. How can you explain these apparent contradictions? Due January 3-7 If a teenager and a half can eat a pizza and a half in a day and a half, how many pizzas can twelve teenagers eat in three days? Due January 10-14 Determine all values of k so that 2x + 1 is a factor of 2x^2 + 7x + k. Due January 18-21 The third term of an arithmetic sequence is 15, and the fifth term is 23. What is the first term? Due January 24-28 What is the sum of all the digits of all the positive integers that are less than 100? Due January 31 - February 4 The digits 1, 3, 4, 6, 8, and 9 are each used exactly once to form three two-digit primes. What is the sum of the three prime numbers? Due February 7-11 Matthew and Matilda want to buy a set of DVDs. Matthew has \$47 less than the purchase price, and Matilda has \$2 less. If they pool their money, they still do not have enough to buy the DVDs. If the set costs an integral number of dollars, what is its price? Due February 14-18 How many different positive integers can you form using only the digits 1, 2, 3, and 4 if each digit can be used at most once in any number? Due February 28 - March 4 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 March 7-11 The first and seventh terms of a sequence are both 8. In addition, starting with the third term, each term is the sum of the two previous terms. What is the fifth term? Due March 14-18 Suppose that we know that 10 percent of all Americans prefer dogs to cats and that four out of five people who prefer dogs are men. What proportion of men prefer dogs, and what proportion of women prefer dogs? Due March 21-25 John does not know the pairings of the final eight teams in the NCAA tournament, but he hopes that WKU is one. He finds that the Nashville Banner has picked UCLA, UT, OU, and UK to advance; the Courier-Journal has picked UK, OU, MSU, and UNCC; and the Daily News has picked UK, UT, MSU, and OSU. Determine the pairings of the final eight. Due March 28-Apr 1 Near the end of a party, everyone shakes hands with everybody else. A straggler arrives and shakes hands with only those people whom the straggler knows. Altogether, sixty-eight handshakes occurred. How many people at the party did the straggler know? Due April 4-8 What is the smallest counting number that is divisible by each of the first ten counting numbers? Due April 11-15 Henry's Hamburger Heaven offers its hamburgers with ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties and any assortment of condiments. How many different kinds of hamburgers can be ordered? Due April 25-Apr 29 Using the assumption that the probability that a baby is a boy is 1/2 and the probability that a baby is a girl is 1/2, determine the probability that a family with four children has two boys and two girls. Due May 2-6 Given twenty couples, how many different three-member committees can be formed that do not contain both members of any of these couples? Due May 9-13 Thirty-six students took a final exam on which the passing score was 70. The mean score of those who passed was 78, the mean score of those who failed was 60, and the mean of all scores was 71. How many students did not pass the exam? Due May 16-20 Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible? Due May 23-27 One thousand unit cubes are fastened together to form a large cube with edge length 10 units, each face of which is painted. If the large cube is separated back into unit cubes, how many of these cubes will have paint on at least one face? Due May 31 - June 10 A group of mathematics teachers went to a restaurant. They agreed to split the bill equally. When the bill arrived, two of them discovered that they had forgotten their money. The others in the group agreed to make up the difference by paying an extra \$1.30 each. If the total bill was \$78, how many teachers were in the group? Most problems copyright © 2001-5 National Council of Teachers of Mathematics```