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 use of variables
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Algebra
Problems
Algebra
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Use of Variables
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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
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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.
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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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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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Apple Orchard
- Steve Risberg
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Algebra, difficulty level 2. How many of each kind of apple did the Nomial family pick?
... 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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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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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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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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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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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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Eduardo's Equations
- Steve Risberg Annie Fetter
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Algebra, difficulty level 1. Find all possible integer solutions to a system of four equations in
two variables.
... more>>
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Explaining a Number Trick
- Annie Fetter
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Algebra, difficulty level 1. Use a variable to explain how this number trick works.
... more>>
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Fraction Debate
- Steve Risberg
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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>>
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Generosity
- Ethel Breuche
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Algebra, difficulty level 2. Three generous friends, each with some cash, redistribute their money.
... more>>
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Make the Save!
- Steve Risberg
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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>>
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Mind Reading
- Annie Fetter
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Algebra, difficulty level 1. Use variables to show how a number-based "magic trick" works.
... more>>
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The Operations Grid
- Annie Fetter
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Algebra, difficulty level 2. Use variables to explore whether this grid works for the four basic operations.
... more>>
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Reverse It!
- Annie Fetter Steve Risberg
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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>>
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September Squares
- Cynthia Lanius and Steve Risberg
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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>>
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A Surprising Sequence
- Steve Risberg
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Algebra, difficulty level 2. In a Fibonacci sequence, the first number is 1 and the tenth number is
111. Find the second number.
... more>>
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Teeter-Toddlers
- Steve Risberg
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Algebra, difficulty level 1. Two kids of different weights balance on a seesaw. How far from the
center is each one sitting?
... more>>
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Vexing Variables
- Steve Risberg
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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>>
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What Time Is It?
- Steve Risberg
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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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