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Browse all Algebra Problems of the Week
Participation in the Algebra Problems of the
Week allows teachers and students to address the
NCTM
Problem Solving Standard for Grades 9-12, enabling students to
build new mathematical knowledge through problem solving; solve problems
that arise in mathematics and in other contexts; apply and adapt a
variety of appropriate strategies to solve problems; and monitor and
reflect on the process of mathematical problem solving.
For background information elsewhere on our site, explore the
High School Algebra
area of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Basic Algebra
in our Internet Mathematics Library.
Access to these problems requires a Membership.
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Sam and Teri's Bank Accounts
- Terry Trotter
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Algebra, difficulty level 1. Sam and Teri have bank accounts. Sam always withdraws money; Teri always saves it. When will they have equal balances, or will they?
... more>>
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A Sequence of Numbers
- Asher Walkover
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Algebra, difficulty level 2. Find the second number in a Fibonacci-like series.
... more>>
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Shanell's Holiday Treats
- Terry Trotter
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Algebra, difficulty level 3. Given some data about purchasing fancy nuts for cooking, find the total cost of buying one pound of each type.
... more>>
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Ships Ahoy!
- Terry Trotter
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Algebra, difficulty level 1. One-third of a fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were later lost in a storm. The 24 remaining ships sailed home. How many ships were there before the engagement?
... more>>
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A Space Diagonal
- Terry Trotter, MATHCOUNTS
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Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
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The Spider and the Fly
- J. A. H. Hunter
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Algebra, difficulty level 2. A spider presents a challenge to a fly: solve a math problem and escape!
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The Spiral on the Can
- Ethel Breuche
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Algebra, difficulty level 3. By using the Pythagorean theorem, students can find the length of the spiral painted on a can.
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Splitting a Square
- Terry Trotter
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Algebra, difficulty level 3. A square is drawn on a coordinate plane with vertices P(1, 0), Q(2, 0), R(2, 1) and S(1, 1). A line is drawn from the origin that cuts the square into two sections whose areas are in a ratio of 2:1. What's the equation of the "cutting" line?
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The Straggler Shakes Hands
- Melissa Kennedy, Susan Rose, Ethel Breuche
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Algebra, difficulty level 3. There were one hundred forty-one handshakes in all. How many people did the straggler know? This puzzle involves a quadratic expression and triangular numbers.
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Susita's Savings Account
- Terry Trotter
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Algebra, difficulty level 2. Find the original balance in Susita's savings account.
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A Tale of Two Intercepts
- Terry Trotter
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Algebra, difficulty level 3. Find the distance between two y-intercepts.
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Tele-Plus
- Terry Trotter
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Algebra, difficulty level 1. Find the cost of one phone that is part of a three-in-one communications package deal.
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Tennis Anyone?
- Ethel Breuche
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Algebra, difficulty level 1. Use algebra, inequalities, and ratios to find the greatest number of matches a player could have won before the weekend to achieve the win ratio of .503 after the weekend.
... more>>
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That's Some Sequence!
- Terry Trotter
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Algebra, difficulty level 4. Find the product of 3 terms of an unusual sequence.
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Three Consecutive Integers
- Annie Fetter
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Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers.
... more>>
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The Three Jelly Bean Jars
- Terry Trotter
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Algebra, difficulty level 2. Three brothers buy jelly beans. The jelly beans are in jars that are three different sizes. How many jelly beans does each brother buy?
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Tiffany's Triumphs
- Terry Trotter
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Algebra, difficulty level 1. Given the number of games that Tiffany has played so far and the number that she has won, how many games would she have to win in a row to get her winning percentage up to 60%?
... more>>
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To Grandmother's House We Go
- Ethel Breuche
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Algebra, difficulty level 4. Red Riding Hood goes to visit Grandmother for the holidays at the same time that Grandmother heads out to visit Red. What is the ratio of their speeds?
... more>>
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Touchdown Toddlers
- Terry Trotter
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Algebra, difficulty level 2. Two little boys run an unusual race on a professional football field, and everybody comes out a winner!
... more>>
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Triangle Probability
- Annie Fetter
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Algebra, difficulty level 3. A point is randomly selected from within a triangle with vertices at (0,0), (0,4) and (6,0). What is the probability that the x-coordinate of the selected point is less than the y-coordinate?
... more>>
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A Triangle's Area
- Canadian Open Math Challenge 1999 via Tim Lang
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Algebra, difficulty level 3. Find the "b" values of two lines needed to form two congruent triangles of a given area.
... more>>
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Triangular Number Identities
- Terry Trotter
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Algebra, difficulty level 3. Prove two famous theorems of ancient number theory: the sum of any two consecutive triangular numbers is a square number, and the product of 8 and any triangular number, increased by 1, is a square number.
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Tribonacci
- Terry Trotter
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Algebra, difficulty level 3. Find the second and third terms of a "Tribonacci" sequence.
... more>>
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Trick-or-Treat Box
- Terry Trotter
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Algebra, difficulty level 1. Harvey and his classmates make trick-or-treat boxes in math class and use a special formula to find the volumes.
... more>>
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Two for Two
- Annie Fetter
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Algebra, difficulty level 3. Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers?
... more>>
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Two for Two More
- Annie Fetter
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Algebra, difficulty level 3. Two numbers have a ratio of 4:3. The greater number is 60 more than 8 times their difference. What could the two numbers be?
... more>>
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Two Ladders
- Terry Trotter
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Algebra, difficulty level 2. Find the lengths of two ladders, then find their "differences."
... more>>
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The Unhappy Carpenter
- Ethel Breuche
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Algebra, difficulty level 1. A carpenter agrees to be paid a certain amount of money when she works, and to repay money on the days she doesn't work. Find the number of days she worked if she earned $77.00.
... more>>
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Up the Down Elevator
- Ethel Breuche
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Algebra, difficulty level 2. Juanita has to use a freight elevator to deliver packages but can use the passenger elevator to return. What is her average speed for the entire trip?
... more>>
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Valentine Candy
- Ethel Breuche
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Algebra, difficulty level 2. A vendor who sells Valentine candy boxes wants to raise the price. For every twenty-five-cent increase he loses two customers. At what price should he sell the boxes to achieve the maximum profit?
... more>>
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The Variable Rectangle
- Terry Trotter and Friends
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Algebra, difficulty level 1. Increase a rectangle's width and decrease its length each by 1 and the area is decreased by 4. But decrease its width by 1 and increase its length by 2, and the area is increased by 16. What's the area of the original rectangle?
... more>>
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Walter's Weird Wages
- Terry Trotter
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Algebra, difficulty level 2. Walter's eccentric parents give their son his housework wages in a strange way. Can you determine how much he receives?
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The Way the Crazy Crow Flies
- Janet Bowers
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Algebra, difficulty level 3. A crazy crow flies back and forth between two trains that are approaching each other on parallel tracks. How far does the crow fly?
... more>>
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Weighing Kittens
- Terry Trotter
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Algebra, difficulty level 2. Given some facts, figure out how many ounces each of seven kittens weighs.
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The Weight of Bart's Brick
- Terry Trotter
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Algebra, difficulty level 1. Bart was asked by his construction foreman about the weight of a brick. Bart's answer befuddled his boss. (But not you.)
... more>>
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What's My Angle?
- Terry Trotter
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Algebra, difficulty level 3. Using concepts of vertical angles and supplementary angles, solve two quadratic expressions to find the measure of a given angle.
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What's My Line?
- Terry Trotter
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Algebra, difficulty level 1. Given a set of eight points in the Cartesian plane, find the three that are collinear.
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What's the Score?
- Terry Trotter
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Algebra, difficulty level 2. Find the final score of the football game between the Falcons and the Bears.
... more>>
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What's the Temperature
- Annie Fetter
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Algebra, difficulty level 1. At what temperature do you get the same answer, regardless of
whether
you use the Fahrenheit or the Celsius scale?
... more>>
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What's what?
- Terry Trotter (author unknown)
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Algebra, difficulty level 2. A poetical puzzle to ponder about: "What is WHAT?"
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Winter Gold
- Terry Trotter
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Algebra, difficulty level 2. Given some clues, figure out how many gold medals were won by each country.
... more>>
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The World's Meanest Math Teacher
- Bill Graham
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Algebra, difficulty level 3. Students seated around a circular table are being systematically eliminated. What's the rule to follow to be the last one eliminated?
... more>>
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X Marks the Spot
- Terry Trotter
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Algebra, difficulty level 3. A Spanish pirate buries his treasure on an island in a very mathematical manner. Can you locate the "X" spot?
... more>>
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