Math Forum - Problems Library - Algebra, Use of Variables

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Use of Variables
These problems involve using a variable to represent an unknown quantity and making manipulations of the variables at an introductory algebra level. The problems are suitable for the beginning of an introductory algebra class.

Related Resources
Interactive resources from our Math Tools project:
   Algebra: Use of Variables
The closest match in our Ask Dr. Math archives:
   High School: Algebra
NCTM Standards:
   Algebra Standard for Grades 9-12

Access to these problems requires a Membership.

A 2-for-1 Lunch - Marsha Hurwitz
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>>

Alvin's Theorem - Terry Trotter
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>>

Apple Orchard - Steve Risberg
Algebra, difficulty level 2. How many of each kind of apple did the Nomial family pick? ... more>>

Are You Ready for Some Football? - Steve Risberg
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>>

As the Crow Flies - Terry Trotter
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>>

Baffling Brother - Steve Risberg
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>>

Battle of the Bands - Terry Trotter
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>>

Bowling Buddies - Steve Risberg
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>>

Boxes of Cereal - Steve Weimar
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>>

Calendar Calculations - Steve Risberg
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>>

Count Your Change - Steve Risberg & Terry Trotter
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>>

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>>

Explaining a Number Trick - Annie Fetter
Algebra, difficulty level 1. Use a variable to explain how this number trick works. ... 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>>

Generosity - Ethel Breuche
Algebra, difficulty level 2. Three generous friends, each with some cash, redistribute their money. ... 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>>

Mind Reading - Annie Fetter
Algebra, difficulty level 1. Use variables to show how a number-based "magic trick" works. ... more>>

The Operations Grid - Annie Fetter
Algebra, difficulty level 2. Use variables to explore whether this grid works for the four basic operations. ... more>>

Reverse It! - Annie Fetter Steve Risberg
Algebra, difficulty level 1. Find a two-digit number such that when you reverse the digits and add the new number to the original one, the sum is 154. ... 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 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>>

Teeter-Toddlers - 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>>

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>>

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>>

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