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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.

Dinner at Pepe's
 Steve Risberg

Algebra, difficulty level 1. Three friends share a pizza and sodas. Given information about the
portion of the bill each one paid, determine the total cost of
the meal.
... more>>

A Dog, a Hog, and a Frog
 Redwood Empire Mathematics Tournament

Algebra, difficulty level 2. Three animal friends want to cross a big swamp. How wide is that swamp?
... more>>

Donald Duck's Trip
 Terry Trotter

Algebra, difficulty level 2. What fractional part of Donald's trip had he traveled by 4:00 P.M.?
... more>>

Don't Be Square
 Ethel Breuche

Algebra, difficulty level 1. Use pattern recognition and square roots to find the sum of two numbers.
... more>>

Dot.com Derby
 Terry Trotter

Algebra, difficulty level 2. Three "dots" run a race around a circular track in an unusual manner. You must determine the winners in two categories.
... more>>

Driving to Work
 Annie Fetter

Algebra, difficulty level 2. Tracey drives to work at 40 mph and is 1 minute late. If she leaves at the same time and drives 45 mph, she'll be 1 minute early. How far does Tracey live from work?
... more>>

Eduardo's Equations
 Steve Risberg Annie Fetter

Algebra, difficulty level 1. Find all possible integer solutions to a system of four equations in
two variables.
... more>>

Elbert's Equation
 Steve Risberg

Algebra, difficulty level 3. Use exponent properties, absolute value, and quadratic equations to
find the six solutions to Elbert's equation.
... more>>

Escalation
 Melissa Kennedy

Algebra, difficulty level 2. A rate, time, distance problem that involves finding the number of steps on an escalator.
... more>>

The EV Function
 Terry Trotter

Algebra, difficulty level 2. Given a function's definition, find the input (argument) value that yields a certain output value.
... more>>

Examining an Equation
 Steve Risberg

Algebra, difficulty level 2. Find integer solutions to an equation in two variables.
... more>>

An Expanding Circle
 Steve Risberg

Algebra, difficulty level 2. When the radius of a circle increases by 6 inches, the area increases
by 125%. Find the original radius.
... more>>

Explaining a Number Trick
 Annie Fetter

Algebra, difficulty level 1. Use a variable to explain how this number trick works.
... more>>

Factor Bingo
 Steve Risberg

Algebra, difficulty level 1. You're playing Factor Bingo. Determine what squares on your card you
can cover so far and create a polynomial that will let you win on the
next turn.
... more>>

Family Fun
 Molly Stanley and Steve Risberg

Algebra, difficulty level 3. The Gonzalez family is competing in a relay race where each family
member runs one lap. How long did it take Vicenta to run hers?
... more>>

Filling Glasses
 Annie Fetter

Algebra, difficulty level 2. Match up each of the three glasses with the graph that best describes the height of the water in the glass over time, when the glass is filled with water at a constant rate.
... more>>

Filling the Aquarium
 Terry Trotter

Algebra, difficulty level 2. A workman at a zoo has to clean an aquarium, but forgets to do an important task, thus causing a problem (for us).
... more>>

Finding a TwoDigit Number
 Annie Fetter

Algebra, difficulty level 2. Find a twodigit number such that if you reverse its digits to get another twodigit number, then add this to the original number, you get 143.
... more>>

Flatland Soldiers
 Terry Trotter

Algebra, difficulty level 1. Find the size of the vertex angle of a soldier in the world of Flatland, a famous book by Edwin A. Abbott.
... more>>

Flying Off the Shelves
 Steve Risberg

Algebra, difficulty level 1. The new soundtrack album from the movie Ray is selling like hotcakes!
Given some information about the sales over three days at Tip Top
Tunes, can you determine how many CDs sold per day?
... more>>

Fording the River
 Lisa and Judy Gardner

Algebra, difficulty level 2. A terrible accident occurred just when the hands of a watch were in a special position. What time was it?
... more>>

Four Men and Some Money
 Daboll

Algebra, difficulty level 1. Four men (A, B, C, & D) are splitting up a quantity of money ($100), and need your help to do it.
... more>>

Fraction Action!
 Steve Risberg

Algebra, difficulty level 2. What happens when you add the denominator to both the numerator and denominator of a fraction?
... more>>

Fraction Debate
 Steve Risberg

Algebra, difficulty level 3. Three students disagree about what happens when you perform a certain operation on a positive proper fraction. Which student do you agree with? Why?
... more>>

From Here to There
 Steve Risberg

Algebra, difficulty level 2. Given descriptions of the rate schedules of a bus, a taxi, and a
shuttle, choose the graphs that best illustrate the cost of riding
each one.
... more>>

The Function Challenge
 Bill Graham

Algebra, difficulty level 2. Arrange a series of functions in the order that will produce the largest output.
... more>>

Funny Ducks
 Ethel Breuche

Algebra, difficulty level 4. These funny ducks always walk exactly three feet from the lily pond. What is the area of the region bounded by their path?
... more>>

Generosity
 Ethel Breuche

Algebra, difficulty level 2. Three generous friends, each with some cash, redistribute their money.
... more>>

Going for the Gold
 Terry Trotter

Algebra, difficulty level 4. Find the number of points that are awarded for each gold, silver, and bronze medal in an athletic competition.
... more>>

Grandpa Jones' Age
 Terry Trotter

Algebra, difficulty level 2. Little George asks how old his grandpa is, and needs your help to find out the answer.
... more>>

The Great Doughnut Caper
 Terry Trotter

Algebra, difficulty level 2. After a number of doughnuts have been switched in their respective boxes, you are to discover the original state of things before the change was made.
... more>>

The Great One
 Terry Trotter

Algebra, difficulty level 2. Indiana Jones found a math problem about the life span of "The Great One" engraved on an old tombstone. How old was the Great One when he died?
... more>>

Gumballs Galore!
 Terry Trotter

Algebra, difficulty level 2. Two famous characters from literature go on a gumball shopping spree.
... more>>

Halloween Night
 Ethel Breuche

Algebra, difficulty level 1. One hundred candy kisses were being distributed, one at a time, to five goblins at my door. The phone rang, and when I came back I didn't remember where I had left off. How did I continue distributing without
starting over?
... more>>

Heating the Tub
 Steve Risberg

Algebra, difficulty level 1. Water in a hot tub is heated. Given two times and the temperature at
those times, find an equation that models the heating process, then
use it to predict temperatures and times as the heating continues.
... more>>

He Shoots! He Scores!
 Annie Fetter, Steve Risberg, & Terry Trotter

Algebra, difficulty level 3. Given a set of equations and inequalities, figure out how many points Bo might have scored in his basketball game.
... more>>

Highway Miles
 Terry Trotter

Algebra, difficulty level 2. Find the number of miles a person travels on a highway, given the number of gallons of gas and the consumption rate.
... more>>

Hiking Mount Hood
 PoW staff

Algebra, difficulty level 1. Don hikes up and down a mountain at various speeds. Choose the graph
that best represents his trip.
... more>>

Hole in One!
 Steve Risberg

Algebra, difficulty level 4. Given the dimensions of a miniature golf hole, use slopes to determine
how Tiger needs to hit his shot to make a hole in one.
... more>>

Holiday Dance
 Steve Risberg

Algebra, difficulty level 2. Two bands are being considered for the holiday dance at Rahkenrole
High School. Each band charges a base fee and an hourly rate. Help
the Student Council compare the bands and find the best deal.
... more>>

HomeMade Valentine Card
 Terry Trotter

Algebra, difficulty level 2. Reuben expresses his affection for his girlfriend by making his own Valentine's Day card, described mathematically.
... more>>

Homer Jones
 Terry Trotter

Algebra, difficulty level 3. Find the area of a certain triangle laid out on a baseball field.
... more>>

Hoop Heroes
 Steve Risberg

Algebra, difficulty level 3. Use inequalities to determine how many points Kylie and Shaniqua each
scored in the championship basketball game.
... more>>

How High Is Enough?
 Terry Trotter

Algebra, difficulty level 3. A right triangle is formed by stretching flexible elastic "legs" sufficiently high. How high must that be?
... more>>

Humphrey's Great Escape
 Bill Graham

Algebra, difficulty level 3. Calculate Humphrey's running speed as he tries to outrun a train across a trestle.
... more>>

Humphrey's Phone Number
 Bill Graham

Algebra, difficulty level 3. Figure out Humphrey's 10digit phone number given various clues about the divisibility of parts of his number.
... more>>

Illuminating Lines
 Annie Fetter

Algebra, difficulty level 2. Match up statements, equations, and sets of points on coordinate planes.
... more>>

It's the Law!
 Terry Trotter

Algebra, difficulty level 3. Explain the two most important laws of exponents, as a good teacher or book might do.
... more>>

Jack and Jill Go Jogging
 Terry Trotter

Algebra, difficulty level 2. Two famous Mother Goose characters take up aerobics, running at some numerical speeds while exercising. How fast can each one jog?
... more>>

Jimmy's Hits
 Terry Trotter & Annie Fetter

Algebra, difficulty level 2. Given information about how many doubles, homers, and singles, figure out how many total hits Jimmy had during his recordbreaking season.
... more>>
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