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Algebra
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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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2002 Is Sum Year!
- Terry Trotter
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Algebra, difficulty level 4. Find an arithmetic sequence the sum of whose terms is 2002.
... more>>
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A 2-for-1 Lunch
- Marsha Hurwitz
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Algebra, difficulty level 2. Two boys had lunch on a two-for-one coupon, plus taxes and tips. What was their percent of savings on the transaction?
... more>>
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The ABC's of Exponents
- Steve Risberg
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Algebra, difficulty level 3. Solve a system of equations involving exponents.
... more>>
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'Ace' Trotter
- Terry Trotter
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Algebra, difficulty level 1. A problem from the sports world regarding free-throw percentages.
... more>>
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Adrienne's Axel
- Leslie Hogben
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Algebra, difficulty level 2. Adrienne, an algebraically inclined figure skater, figures an interesting problem for us.
... more>>
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The Ages of Sigma
- Terry Trotter
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Algebra, difficulty level 1. Find the ages of the three artists who make up the latest singing sensation: Sigma.
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All Wet
- Linda Benton
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Algebra, difficulty level 3. Solve simultaneous equations, find area, and use the Pythagorean theorem and percentages to find the spraying distance needed for a circular sprinkler in a rectangular yard.
... more>>
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Alvin's Theorem
- Terry Trotter
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Algebra, difficulty level 2. Alvin notices that the difference between any two consecutive square
numbers can also be expressed as the sum of consecutive integers.
Can you use algebra to show that this pattern is always true?
... more>>
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Ancestors
- Steve Risberg
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Algebra, difficulty level 2. Find how many ancestors Gene had from various generations going back
in time.
... more>>
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Ant Race
- Terry Trotter
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Algebra, difficulty level 1. Two ants race to a piece of food. Your task is to figure out how far apart they were when the race started.
... more>>
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Apple Orchard
- Steve Risberg
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Algebra, difficulty level 2. How many of each kind of apple did the Nomial family pick?
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Approval Method of Voting
- Ethel Breuche
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Algebra, difficulty level 3. In the country of Algpoweria, eligible voters can cast their votes for two candidates. Based on the clues given, find how many votes each candidate received and the number of eligible voters.
... more>>
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Are We There Yet?
- Terry Trotter
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Algebra, difficulty level 1. Given what fractions of a car trip have been completed at two different times, can you predict when the trip will end?
... more>>
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Are You Positive?
- Steve Risberg
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Algebra, difficulty level 3. Find all values of x that make a rational expression have a positive value.
... more>>
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Are You Ready for Some Football?
- Steve Risberg
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Algebra, difficulty level 2. The Algenauts football team racked up 229 yards rushing in their first
game. Given descriptions of how many yards each of the players ran
for in relation to each other, determine the exact yardage each one had.
... more>>
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As the Crow Flies
- Terry Trotter
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Algebra, difficulty level 1. A percentage of crows sitting on a telephone line leaves, then returns. Find how many crows are present at the end.
... more>>
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At Least This Many
- Terry Trotter
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Algebra, difficulty level 2. Using two data points from the NBA statistics chart, form an equation (y = mx + b style), then use it to predict other data points.
... more>>
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An "Average" Problem
- Terry Trotter
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Algebra, difficulty level 2. Three test grades are removed from a set of scores. You are given the new set's average and a ratio involving the scores removed. What scores have been removed?
... more>>
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Baffling Brother
- Steve Risberg
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Algebra, difficulty level 2. Brandon wows his sister by having her choose a secret number and make
a series of calculations, then telling her what her final answer is.
Can you use variables and algebra to explain how Brandon did it?
... more>>
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Battle of the Bands
- Terry Trotter
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Algebra, difficulty level 3. Students at Rahkenrole High School vote to decide which band should
play at the end-of-year dance. After some students change their
minds about which band to vote for, the result is a tie. Can you
figure out how many students voted?
... more>>
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Blowin' in the Wind
- Steve Weimar Steve Risberg
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Algebra, difficulty level 3. A plane flies a round-trip on a calm day and then flies the same trip
on a windy day. How do the flying times compare?
... more>>
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The Bouncing Ball
- Steve Risberg
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Algebra, difficulty level 1. A ball is dropped from 27 feet and bounces back to 2/3 of the height
from which it fell. Find and use a formula to calculate the height of
the nth bounce.
... more>>
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Bowling Buddies
- Steve Risberg
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Algebra, difficulty level 2. Four friends go bowling and have a small contest. From the clues
given about their scores, can you determine who won the contest?
... more>>
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Bowl-O-Rama!
- Steve Risberg
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Algebra, difficulty level 1. Given information about the number of games two people bowled and how
much each paid, determine the cost of bowling at Bowl-O-Rama.
... more>>
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Boxes of Cereal
- Steve Weimar
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Algebra, difficulty level 2. Lily and Mikey consume their boxes of cereal at different rates. Use
the hints to determine how much cereal is in each child's box.
... more>>
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The Box Supper
- Terry Trotter
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Algebra, difficulty level 3. Find the amount of money that Judy Ann's "beau" paid at the box supper auction for her box of delicious food.
... more>>
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Break the Code!
- Steve Risberg
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Algebra, difficulty level 1. Can you factor the polynomials and use the factors to decipher the
secret message?
... more>>
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Bugs Bunny's Money
- Terry Trotter
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Algebra, difficulty level 2. Find how much Mr. Bugs Bunny is carrying in a money bag, given clues such as the ratio of coins that are pennies and the percentage of coins that are dimes.
... more>>
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Building a Bakery
- Steve Risberg
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Algebra, difficulty level 3. Find the best place to build the bakery so that the delivery miles to the stores are minimized.
... more>>
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Bull's-eye Probability
- Ethel Breuche
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Algebra, difficulty level 3. Find the probability of hitting a circular target board closer to the center.
... more>>
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Burger Inflation?
- Annie Fetter, Terry Trotter, Steve Risberg, and Steve Weimar
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Algebra, difficulty level 2. Given the affect of inflation, is a national-chain hamburger cheaper or more costly than it was in 1970?
... more>>
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Buried Treasure
- Steve Risberg
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Algebra, difficulty level 3. The pirate Algebeard has drawn an unusual treasure map. Can you
determine where his treasure is buried?
... more>>
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Buy This Tune!
- Terry and NCTM's WLME
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Algebra, difficulty level 2. Using data about buying habits of music lovers from 1990 and 1996, predict the results for 2000 and compare those predictions to the actual data.
... more>>
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Calendar Calculations
- Steve Risberg
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Algebra, difficulty level 1. Write variable expressions for dates in a calendar pattern and use your expressions to explore a numeric relationship among those dates.
... more>>
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Calling Long Distance
- Terry Trotter
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Algebra, difficulty level 1. Use simple equations to compare two telephone calling plans.
... more>>
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Capture the Flag!
- Steve Risberg
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Algebra, difficulty level 4. Help the Algebra and Geometry classes at Mathland High find the
equation of a perpendicular bisector to fairly divide the woods for
their game of Capture the Flag.
... more>>
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Carlita's CD Collection
- Terry Trotter, Steve Risberg
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Algebra, difficulty level 2. Carlita describes how many CD's are in her collection in a rather
mathematical way. Can you figure out how many there are?
... more>>
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Cheap Sunglasses
- Steve Risberg
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Algebra, difficulty level 2. Help Gilbert figure out if his idea for making cheap sunglasses with
filter film will work.
... more>>
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Cherokee Creek Checkers Club
- Terry Trotter
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Algebra, difficulty level 1. Until one month ago, the Checkers Club had won 40 of 90 matches so far this year. But last
month they won 3 of every 5 games they played. How many games did
they play last month if their overall winning percentage is now 52%?
... more>>
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The Chip Swap Game
- Ethel Breuche
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Algebra, difficulty level 4. The object of this game is to swap the positions of the different colored chips. Count the number of moves and, as you increase the number of chips, find the general formula.
... more>>
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Choosing Charity
- Steve Risberg
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Algebra, difficulty level 2. A company donates to a relief fund by giving a certain amount plus an
additional amount for each employee who decides to donate. Given two
data points, find the linear equation that defines the company's part
of the total donation.
... more>>
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The Christmas Gifts
- Terry Trotter
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Algebra, difficulty level 2. A grandfather doles out his annual Christmas gifts to his beloved grandchildren in a most unusual way - mathematical, of course.
... more>>
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A Coat of Golden Angels
- Terry Trotter
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Algebra, difficulty level 1. Show how to do scientific notation problems on an 8-digit, four-function calculator.
... more>>
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The Continued Fraction
- Ethel Breuche
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Algebra, difficulty level 4. Find the value of a given continued fraction.
... more>>
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Copying Conundrum
- Annie Fetter
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Algebra, difficulty level 1. Using a copy machine, copy an 8 x 10 inch picture at 80%. Then copy the copy at 80%, and repeat this until you have 5 copies of the original. What's the largest dimension now? What's a formula you could use?
... more>>
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Count Your Change
- Steve Risberg & Terry Trotter
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Algebra, difficulty level 3. I have three times as many nickels as dimes in my pocket. If the
number of coins is reversed, by what percent will the value of the
money in my pocket increase?
... more>>
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Crossed Wires
- Steve Risberg
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Algebra, difficulty level 3. Guy wires support two poles of different heights. Find the height of
their intersection and explore what happens as the distance between
the poles changes.
... more>>
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The Custom of Customs
- Ethel Breuche
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Algebra, difficulty level 2. Two wine merchants enter Paris with their merchandise. They need to pay custom duties. Each pays with francs and with some casks of wine. What is each cask of wine worth and what is the duty on each cask?
... more>>
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A Day at the Fairs
- Terry Trotter via Kraitchik & Chuquet
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Algebra, difficulty level 2. A merchant went selling and buying at three city fairs. Did he make a profit or take a loss?
... more>>
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Diego's Building Block
- Terry Trotter
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Algebra, difficulty level 3. Find the surface area of a rectangular prism, given the volume and information about the dimensions.
... more>>
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