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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.

Porky Pig's Popcorn Diet
 Terry Trotter

Algebra, difficulty level 4. Porky is put on a special diet plan so that he can enjoy his favorite snack: POPCORN!
... more>>

Powerfull Fractions
 Terry Trotter

Algebra, difficulty level 1. Given the expression (A/B)^C + (D/E)^F + (G/H)^I, substitute the digits 1 through 9 for the variables so that the simplified value of the expression is an integer.
... more>>

Presidential Approval Rating
 Ethel Breuche

Algebra, difficulty level 3. Students were given a questionnaire. Only 60 percent of the students answered, and of those 55 percent said they approved of the President. What is the maximum number of students who approved of the President?
... more>>

Pressed for Time
 Steve Risberg

Algebra, difficulty level 2. Due to a late breaking story, a newspaper must use both presses to get
an edition printed in time. Find how long it takes to print a normal
edition using only the newer press.
... more>>

The Price of Pollo
 Terry Trotter

Algebra, difficulty level 2. Use a linear equation model to predict a future price of fried chicken.
... more>>

Probability on the Board
 Ethel Breuche

Algebra, difficulty level 3. On a 6 x 6 grid, what is the probability that a marker starting at (0,0) will pass through (3,3) when moved either north or
east?
... more>>

A ProductPlus1
 Terry Trotter

Algebra, difficulty level 3. The product of any four consecutive integers, increased by one, is always a square number. Give at least three instances of that statement and prove that this will always occur by finding an algebraic expression for that "square number."
... more>>

The Professors' Ages
 Terry Trotter

Algebra, difficulty level 3. Find the professors' ages to complete the requested calculation.
... more>>

The Professors' Primes
 Terry Trotter

Algebra, difficulty level 2. Find the product of three prime numbers that three professors pick.
... more>>

Profits and Lots
 Terry Trotter

Algebra, difficulty level 1. A person buys some land, keeps some for himself, divides the rest into lots, and sells them, thus making a profit.
... more>>

Pythagoras and Y2K
 Terry Trotter

Algebra, difficulty level 4. Find Pythagorean triples for which this special year, Y2K (2000), is one of the three numbers in the triple.
... more>>

Radical Rectangle
 Steve Risberg

Algebra, difficulty level 2. Solve a quadratic equation to find the area of a rectangle, expressing
your answer in simplified radical form.
... more>>

Ration Ratios
 Steve Risberg

Algebra, difficulty level 3. Determine the ratio of vegetarian meals to vegetarians at the luncheon.
... more>>

Reciprocals
 Steve Risberg

Algebra, difficulty level 3. Explore the numeric difference between numbers and their reciprocals.
... more>>

Reverse It!
 Annie Fetter Steve Risberg

Algebra, difficulty level 1. Find a twodigit number such that when you reverse the digits and add
the new number to the original one, the sum is 154.
... more>>

Rocket Science
 Steve Risberg

Algebra, difficulty level 1. Given the initial velocity of a model rocket, determine at what time
the rocket attains a certain height.
... more>>

Romance by Rowboat
 Terry Trotter

Algebra, difficulty level 1. Romance on the river motivates a nice upstreamdownstream sort of problem.
... more>>

Round the World on a Wire
 Terry Trotter

Algebra, difficulty level 2. A wire is wrapped around the equator of the earth. Then extra wire is spliced in. Can you walk under the slack that results?
... more>>

Row, Row, Row Your Boat
 Ethel Breuche

Algebra, difficulty level 2. Cassie and Mat are sinking fast on their raft. How fast must Cassie bail so that they don't have to swim to shore?
... more>>

Sam and Teri Revisited
 Terry Trotter

Algebra, difficulty level 3. A bank account depositwithdrawal problem with a difference.
... more>>

Sam and Teri's Bank Accounts
 Terry Trotter

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>>

September Squares
 Cynthia Lanius and Steve Risberg

Algebra, difficulty level 2. Use a variable to explain how you can be given the sum of four dates
that form a block on a calendar and determine what the four dates must be.
... more>>

A Sequence of Numbers
 Asher Walkover

Algebra, difficulty level 2. Find the second number in a Fibonaccilike series.
... more>>

Shanell's Holiday Treats
 Terry Trotter

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>>

Ships Ahoy!
 Terry Trotter

Algebra, difficulty level 1. Onethird of a fleet was captured, onesixth was sunk, and two ships were destroyed by fire. Oneseventh 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>>

Sierpinski Stages
 Steve Risberg

Algebra, difficulty level 2. Find and use patterns to determine the total perimeter of an interesting shape.
... more>>

Skeeball Showdown
 Steve Risberg

Algebra, difficulty level 3. Kira and Daquan each play a game of Skeeball to see who gets the
higher score. Given descriptions of their results in relation to each
other, determine the final score of their match and how many balls
each player rolled.
... more>>

A Space Diagonal
 Terry Trotter, MATHCOUNTS

Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
... more>>

Spell It Out
 Steve Risberg Annie Fetter

Algebra, difficulty level 2. A wordfind problem exploring how sets of points that form lines can
be described by written sentences. An introduction to linear equations
that sets the stage for the standard y = mx + b form.
... more>>

The Spider and the Fly
 J. A. H. Hunter

Algebra, difficulty level 2. A spider presents a challenge to a fly: solve a math problem and escape!
... more>>

The Spiral on the Can
 Ethel Breuche

Algebra, difficulty level 3. By using the Pythagorean theorem, students can find the length of the spiral painted on a can.
... more>>

Splash!
 Steve Risberg

Algebra, difficulty level 1. How many throws did it take each student to sink Mr. Rashanul in the
dunking booth at the carnival?
... more>>

Splitting a Square
 Terry Trotter

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?
... more>>

The Sprats
 Terry Trotter & Lisa Lavelle

Algebra, difficulty level 2. The Sprats go out to dinner three times, and at each meal they order a different combination of two of their three favorite dishes. Given the bill for each meal, determine how much the Sprats' favorites cost individually.
... more>>

The Straggler Shakes Hands
 Melissa Kennedy, Susan Rose, Ethel Breuche

Algebra, difficulty level 3. There were one hundred fortyone handshakes in all. How many people did the straggler know? This puzzle involves a quadratic expression and triangular numbers.
... more>>

Studying the Standings
 Steve Risberg

Algebra, difficulty level 3. Write and solve a system of equations to determine how many points the
Potters have in the World Tiddlywinks League standings.
... more>>

Sums, Quotients, and Remainders
 Terry Trotter

Algebra, difficulty level 3. Given the sum of two numbers and information about the quotient and
remainder when they are divided, find the larger number, then
solve the same sort of problem in a general case.
... more>>

A Surprising Sequence
 Steve Risberg

Algebra, difficulty level 2. In a Fibonacci sequence, the first number is 1 and the tenth number is
111. Find the second number.
... more>>

Susita's Savings Account
 Terry Trotter

Algebra, difficulty level 2. Find the original balance in Susita's savings account.
... more>>

Swapping Marbles
 Lillian Ray, Steve Risberg, and Steve Weimar

Algebra, difficulty level 3. Three kids swap marbles in an interesting way. After the swapping, which of the three had gained the most marbles? How many did they gain?
... more>>

Take Me Out to the Ballgame
 Annie Fetter

Algebra, difficulty level 4. Determine how many innings a pitcher has thrown as his Earned Run Average changes during a game.
... more>>

A Tale of Two Intercepts
 Terry Trotter

Algebra, difficulty level 3. Find the distance between two yintercepts.
... more>>

Taxi!
 Steve Risberg

Algebra, difficulty level 1. Taxi fares in Lineville are based on a linear equation. Given the
costs and distances of two rides, find the equation and use it to
answer several questions.
... more>>

TeeterToddlers
 Steve Risberg

Algebra, difficulty level 1. Two kids of different weights balance on a seesaw. How far from the
center is each one sitting?
... more>>

Teeter Trio
 Steve Risberg

Algebra, difficulty level 1. Find a function that expresses where a child sits on a seesaw in terms
of her weight.
... more>>

Teeter Troop
 Steve Risberg

Algebra, difficulty level 3. Four animals are balancing a seesaw. Can you determine how much each
one weighs?
... more>>

TelePlus
 Terry Trotter

Algebra, difficulty level 1. Find the cost of one phone that is part of a threeinone communications package deal.
... more>>

Tennis Anyone?
 Ethel Breuche

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>>

Texting 1, 2, 3
 Steve Risberg

Algebra, difficulty level 2. Determine the pricing of Kheri's cell phone texting plan.
... more>>
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