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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.

Johnny's Orchards
 Terry Trotter

Algebra, difficulty level 3. Johnny Appleseed plants three rectangular orchards of various shapes.
If each orchard holds the same number of seeds, how many seeds did he
plant?
... more>>

The Joke
 Steve Risberg

Algebra, difficulty level 1. A joke circulates the Internet via email, with each recipient
forwarding it on to 8 friends. Find a formula to represent the number
of emails sent out at any stage of the forwarding, and use your
formula to answer some questions.
... more>>

Judy and Jen's Garden Problem
 Terry Trotter

Algebra, difficulty level 2. Judy and her daughter Jen make up math problems while working in their vegetable garden.
... more>>

Kristina's Code
 Suzanne Alejandre & Steve Weimar

Algebra, difficulty level 1. Use the four equations that Kristina wrote to figure out her two unknown numbers.
... more>>

Laser Tag
 Steve Risberg

Algebra, difficulty level 3. Help Karsten determine where he needs to shoot his laser in order to
hit his friend Jorge in a game of laser tag.
... more>>

The Length of Larry's Rectangle
 Larry Sue

Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him?
... more>>

Let It Snow!
 Steve Risberg

Algebra, difficulty level 3. Use the given statements to determine how many clear days there were
in a recent span of snowy days.
... more>>

Letter Jackets
 Steve Risberg

Algebra, difficulty level 4. A company makes jackets that show support for your school. Given
information on the time needed to make each of two models and the
profit earned for selling them, determine how many of each the company
should make each day to maximize the profit.
... more>>

Lettuce for Sale
 Ethel Breuche

Algebra, difficulty level 1. Using a linear equation, determine the number of heads of lettuce sold on Monday.
... more>>

Lieutenant Stone's Troops
 Terry Trotter

Algebra, difficulty level 2. Find the number of soldiers, performing in a formal military ceremony, who were marching in various rectangular arrangements.
... more>>

Line Logic
 Steve Risberg

Algebra, difficulty level 1. Given five statements, find an equation of a line that makes four of the statements true and one false.
... more>>

Lost in Mathland
 Steve Risberg

Algebra, difficulty level 2. Zach and Zeke get separated while hiking in Mathland, where roads
are named with equations. Zeke is at the intersection of three roads
 can you help Zach determine where he is?
... more>>

Louis And Boris Get Even
 Ethel Breuche

Algebra, difficulty level 2. After taking their respective hormone pills, Louis is growing and Boris is shrinking. How long will it take before they become the same height?
... more>>

Lucie and Daryl's Bike Ride
 Terry Trotter

Algebra, difficulty level 2. A sister and brother who ride bikes provide us with a math challenge concerning distance, rate, and time.
... more>>

Make the Save!
 Steve Risberg

Algebra, difficulty level 1. A hockey goalie has saved 112 out of 131 shots so far this season.
How many consecutive shots does she need to save to raise her save
percentage to .900?
... more>>

Making Triangles
 Steve Risberg

Algebra, difficulty level 4. The lengths of three segments are represented by (n + 2)^2, 9, and n(n
+ 5). Determine for what values of 'n' these three segments can be
used to form a triangle.
... more>>

Many or Money?
 Steve Risberg

Algebra, difficulty level 3. Help the Student Council decide how much to charge for tickets to the concert.
... more>>

Marathon Mitch
 Terry Trotter

Algebra, difficulty level 2. Mitch runs a road race and increases speed twice during the race.
Given his total finishing time, determine his standard running rate.
... more>>

Marsha's Triangle
 Marsha Hurwitz

Algebra, difficulty level 3. Find the area of an isosceles triangle whose two legs are on the x and y axes and whose hypotenuse passes through the point (c,d).
... more>>

Math Club Mystery
 Steve Risberg

Algebra, difficulty level 2. Given information about the total number of people, ticket prices, and
money spent, determine how many students, teachers, and parents went
on the Math Club field trip.
... more>>

Math on the Midway
 Steve Risberg

Algebra, difficulty level 1. Can you win the carnival midway math game by finding a pattern in
the numbers?
... more>>

Maxwell's Mowing
 Terry Trotter

Algebra, difficulty level 1. Maxwell mows rectangular lawns by mowing around the rectangle, leaving a smaller rectangle. If the lawn is 200 feet by 120 feet, how wide a swath has he mowed so far if his mower runs out of gas 1/4 of the way through?
... more>>

The Mensa Toy Store
 Terry Trotter

Algebra, difficulty level 2. The prices are strange in this store. Can you decipher them?
... more>>

Midpoint Magic
 Terry Trotter

Algebra, difficulty level 4. Connecting the midpoints of a general quadrilateral yields a special new foursided figure. What is it?
... more>>

Milly Miffin's Muffins
 J. A. H. Hunter

Algebra, difficulty level 2. Milly Miffin et al. are muffin makers extraordinaires, and they make muffins mathematically, too. The question is, how many?
... more>>

Mind Reading
 Annie Fetter

Algebra, difficulty level 1. Use variables to show how a numberbased "magic trick" works.
... more>>

Missing Angle Mystery
 Terry Trotter

Algebra, difficulty level 2. Help Detective Sam Spade solve a robbery of valuable polygons from Mrs. Hempstead's famous collection.
... more>>

Motorcycle Daredevil
 Terry Trotter

Algebra, difficulty level 4. A motorcycle stunt person needs some math equation work to calculate her most daring feat: jumping between ramps at high speeds.
... more>>

Mr. Cramer's Cousins
 Terry Trotter

Algebra, difficulty level 3. Find the ages of two young men by using Cramer's Rule to solve a system of linear equations.
... more>>

Mr. Fachtore's Gardens
 Steve Risberg

Algebra, difficulty level 1. Mr. Fachtore has decided to plant two gardens this year  one
rectangular and one square. Given algebraic expressions for the areas
of the gardens, find algebraic expressions for their dimensions.
... more>>

Mr. Green's Birthday
 Ethel Breuche

Algebra, difficulty level 1. Mr. Green has a birthday but will not tell his age directly. Can you figure out his age based on the clues?
... more>>

Music Survey
 Ethel Breuche

Algebra, difficulty level 2. Students were surveyed about their favorite music groups. Some liked Hole, others U2, and still others Third Eye Blind. Given all the clues, how many students were surveyed, how many preferred only U2, and how
many liked exactly two of the groups?
... more>>

My Bag of Marbles
 Terry Trotter

Algebra, difficulty level 2. Find the probability of drawing a blue marble after additional marbles have been placed in a bag.
... more>>

My Grandfather's Clock
 Ethel Breuche

Algebra, difficulty level 3. Listening to the chimes, what would be the
longest time I would have to wait to be sure of exactly what time it was?
... more>>

The Mystery Quadrilateral
 Annie Fetter & Dr. Math

Algebra, difficulty level 2. Three consecutive sides of a quadrilateral are 2, 6, 9, and x. If
the
diagonals are perpendicular, what's x?
... more>>

My Three Dogs
 Terry Trotter

Algebra, difficulty level 2. Given information about the weights of three pairs of dogs, figure out the dogs' individual weights.
... more>>

Number, Please!
 Terry Trotter

Algebra, difficulty level 4. Given two telephone calling plans, find the point at which the monthly bills would be the same.
... more>>

The Operations Grid
 Annie Fetter

Algebra, difficulty level 2. Use variables to explore whether this grid works for the four basic operations.
... more>>

Operation Warmup
 Annie Fetter

Algebra, difficulty level 2. Find all possible ordered pairs that are solutions to four given equations.
... more>>

Painting Partners
 Terry Trotter

Algebra, difficulty level 1. Two house painters combine their skills and talents to make short order of a painting job.
... more>>

Paper and the Moon
 Ethel Breuche

Algebra, difficulty level 4. Students need to express their answers in scientific notation and know how to work in the metric system as well as do conversions to answer this papertearing problem.
... more>>

Parakeets on Parade
 Terry Trotter

Algebra, difficulty level 2. A flock of parakeets flies a round trip to the feeding ground and
back. Given the total time and distance of the round trip, and the
speed of the wind in each direction, find the flying speed of the
parakeets.
... more>>

Partners in Pizza
 Terry Trotter

Algebra, difficulty level 2. Three friends share the cost of a pizza. How much does each contribute?
... more>>

Peanuts and Cashews
 Terry Trotter

Algebra, difficulty level 1. Find the proper mixture of nuts that have a certain price rate to be sold in the nut store.
... more>>

Perfect Apples
 Melissa Kennedy

Algebra, difficulty level 2. Of 6000 apples, we have some that are too small, some too green, and others that are bruised. How many are perfect apples?
... more>>

PhoneOGraph Phollies
 Bill Graham

Algebra, difficulty level 2. Students are asked to use algebra to compare three telephone calling plans to determine at what number of calls each plan would be preferable.
... more>>

A Phoney Deal?
 Steve Risberg

Algebra, difficulty level 2. Compare two cell phone pricing plans to determine for how many minutes
of calls per month each one is the better deal.
... more>>

Pizza Puzzle
 Steve Risberg

Algebra, difficulty level 1. Given two pricing examples, determine a general equation for the cost
of a Giordano's Giant gourmet pizza.
... more>>

Polynomial Power
 Steve Risberg

Algebra, difficulty level 3. Given the value of one variable expression, can you use it to find the value of others?
... more>>

Polynomial Puzzler
 Steve Risberg

Algebra, difficulty level 2. Given four polynomials, find an expression that uses each of them
once, involves multiplication, addition and subtraction, and results
in a given binomial when simplified.
... more>>

Poolish Pride?
 Steve Risberg

Algebra, difficulty level 3. Two competitive brothers build rectangular pools of similar shape but
different size. Given some information relating the lengths and
widths, find the area of the larger pool.
... more>>
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