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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 912, 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.

That's Interesting!
 Steve Risberg

Algebra, difficulty level 3. Two men follow different strategies for saving money. Who winds up
with more?
... more>>

That's Some Sequence!
 Terry Trotter

Algebra, difficulty level 4. Find the product of 3 terms of an unusual sequence.
... more>>

The Coordinate Carousel
 Steve Risberg

Algebra, difficulty level 3. Mrs. Nomial is watching her daughters on the carousel and notices
something interesting. Determine how far away from the edge of the
carousel she is standing.
... more>>

The Great Northern Triathlon
 Steve Risberg

Algebra, difficulty level 2. Sven skis, skates, and snowshoes in the winter triathlon. Use the
given information to determine how fast he snowshoes.
... more>>

Three Consecutive Integers
 Annie Fetter

Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers.
... more>>

The Three Jelly Bean Jars
 Terry Trotter

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?
... more>>

Throw It Down!
 Steve Risberg

Algebra, difficulty level 3. Kelvin leaps high to dunk a basketball. How long are his hands high
enough above the rim for him to dunk?
... more>>

Tiffany's Triumphs
 Terry Trotter

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>>

Time Trial Triumphs
 Steve Risberg, Terry Trotter, and Annie Fetter

Algebra, difficulty level 2. At 9:05 a.m. Ernesto starts riding at a speed of 440 yards per
minute. At 9:20 a.m. Johnny starts riding, but he's going 20% faster
than his little brother. At what time, to the nearest minute, will
Johnny catch Ernesto?
... more>>

To B or Not To B
 Steve Risberg

Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the
ratio of B's to total letters in the nth term.
... more>>

To Grandmother's House We Go
 Ethel Breuche

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>>

Touchdown Toddlers
 Terry Trotter

Algebra, difficulty level 2. Two little boys run an unusual race on a professional football field, and everybody comes out a winner!
... more>>

Triangle Possibilities
 Steve Risberg

Algebra, difficulty level 2. Given information about side lengths of a triangle, determine possible dimensions.
... more>>

Triangle Probability
 Annie Fetter

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 xcoordinate of the selected point is less than the ycoordinate?
... more>>

A Triangle's Area
 Canadian Open Math Challenge 1999 via Tim Lang

Algebra, difficulty level 3. Find the "b" values of two lines needed to form two congruent triangles of a given area.
... more>>

Triangular Number Identities
 Terry Trotter

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.
... more>>

Tribonacci
 Terry Trotter

Algebra, difficulty level 3. Find the second and third terms of a "Tribonacci" sequence.
... more>>

Tribonacci Tribulation
 Steve Risberg

Algebra, difficulty level 2. Given data describing a tribonacci sequence, find a missing number in
the sequence.
... more>>

TrickorTreat Box
 Terry Trotter

Algebra, difficulty level 1. Harvey and his classmates make trickortreat boxes in math class and use a special formula to find the volumes.
... more>>

Two by Canoe
 Annie Fetter

Algebra, difficulty level 3. Figure out what time Tashawn and Forrest need to start back downstream after paddling upstream for two days if they need to meet Forrest's mother at 4 pm on the third day.
... more>>

Two for Two
 Annie Fetter

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>>

Two for Two More
 Annie Fetter

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>>

Two Ladders
 Terry Trotter

Algebra, difficulty level 2. Find the lengths of two ladders, then find their "differences."
... more>>

The Unhappy Carpenter
 Ethel Breuche

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>>

Up the Down Elevator
 Ethel Breuche

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>>

Valentine Candy
 Ethel Breuche

Algebra, difficulty level 2. A vendor who sells Valentine candy boxes wants to raise the price. For every twentyfivecent increase he loses two customers. At what price should he sell the boxes to achieve the maximum profit?
... more>>

The Variable Rectangle
 Terry Trotter and Friends

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>>

A Variable Triangle
 Steve Risberg

Algebra, difficulty level 4. Given a triangle with side lengths of x + 2, x + 3, and 11, what can
we conclude about x?
... more>>

Vexing Variables
 Steve Risberg

Algebra, difficulty level 3. Use two algebraic statements involving three variables to find the
numeric value of the ratio of two of those variables.
... more>>

Voter Turnout
 Steve Risberg

Algebra, difficulty level 2. A group of students collected data on voter turnout for the recent
election and plotted graphs broken down by age groups. Can you match
each age group with its graph?
... more>>

Walter's Weird Wages
 Terry Trotter

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?
... more>>

The Way the Crazy Crow Flies
 Janet Bowers

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>>

Weighing Kittens
 Terry Trotter

Algebra, difficulty level 2. Given some facts, figure out how many ounces each of seven kittens weighs.
... more>>

The Weight of Bart's Brick
 Terry Trotter

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>>

What's My Angle?
 Terry Trotter

Algebra, difficulty level 3. Using concepts of vertical angles and supplementary angles, solve two quadratic expressions to find the measure of a given angle.
... more>>

What's My Line?
 Terry Trotter

Algebra, difficulty level 1. Given a set of eight points in the Cartesian plane, find the three that are collinear.
... more>>

What's the Difference?
 Steve Risberg

Algebra, difficulty level 3. Does multiplying a number by four always give you a greater number
than you started with?
... more>>

What's the Point?
 Steve Risberg

Algebra, difficulty level 3. Find all points on a given line such that they are a specified
distance from two points in the plane.
... more>>

What's the Score?
 Terry Trotter

Algebra, difficulty level 2. Find the final score of the football game between the Falcons and the Bears.
... more>>

What's the Temperature
 Annie Fetter

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>>

What's what?
 Terry Trotter (author unknown)

Algebra, difficulty level 2. A poetical puzzle to ponder about: "What is WHAT?"
... more>>

What Time Is It?
 Steve Risberg

Algebra, difficulty level 3. Determine the angle between the hands of a clock at certain times,
and
find the times that generate a particular angle.
... more>>

Winter Gold
 Terry Trotter

Algebra, difficulty level 2. Given some clues, figure out how many gold medals were won by each country.
... more>>

The World's Meanest Math Teacher
 Bill Graham

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>>

Wreck Tangle
 Steve Risberg

Algebra, difficulty level 2. When the width of a given rectangle is tripled and the length is
doubled, the perimeter increases by 92 cm. Find the area of the
original rectangle.
... more>>

X Marks the Spot
 Terry Trotter

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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