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Word Problems

Browse Middle School Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Direct and indirect variation.
    Inequalities and negative numbers.
    Positive/negative integer rules.
    Solving simple linear equations.

Calendar Puzzle [12/02/1999]
A student cuts a 3x3 square from a calendar page. If the sum of the nine dates is divisible by 19, what is the date in the lower left-hand corner of the square?

Can Police Clock Speeding Car? [06/30/2003]
Car A travels 3 miles at an average speed of 87 mph. Car B begins the same distance from an initial speed of 0, but accelerates from 0-100 mph in 14 seconds. What must the maximum speed of Car B be in order to catch up to Car A at the end of the 3 miles?

Can Variables Be Capital Letters? [09/19/2006]
Can you use capital letters for variables, like X, or does it always have to be x?

Car Laps [01/26/2001]
On a race track, one car travels 5 laps a minute and another car travels 8 laps a minute. How long will it be before the second car laps the first?

Cars Leaving at Different Times [09/28/2003]
Two cars leave a garage traveling in opposite directions. One car leaves at 8 am and averages 60 mph. The other car leaves at 9 am and averages 50 mph. At what time will they be 225 miles apart?

Challenging Algebra Age Problem [02/29/2004]
A man has nine children whose ages are at an exact interval. The sum of the squares of the ages of each is the square of his own age. What is the age of each child and the man?

Checking Equations [01/30/2001]
I know how to solve an equation, but I can't figure out how to check it.

Combining Positive and Negative Exponents [06/30/1999]
When you simplify exponential expressions using the power rule, how do you combine positive and negative exponents in the numerator and denominator?

Common PEMDAS Errors [12/28/2001]
What does PEMDAS mean?

Comparing Numbers: Two Equations, Two Unknowns [01/14/1998]
One number is 25 percent of another. The larger number is 12 more than the smaller. What are the numbers?

Comparison of On-line Rates [5/20/1996]
Jack is interested in two on-line companies, Easy Comp and Destruct Comp...

Completing the Square: How Does it Work? [01/20/1999]
Can you explain why completing the square works? How exactly do you do it?

Completing the Square to Solve Quadratic Equations [12/21/1998]
Steps for solving quadratic equations.

Completing the Square Using a Diagram [11/09/1999]
How can I draw a diagram that represents the "completing the square" operation of x^2 - 6x + ...?

Complicated Age Problem [02/04/2002]
Eight years ago Mary was half as old as Jane will be when Jane is one year older than Tim will be at that time when Mary will be five times as old as Tim will be two years from now...

Complicated Computation [2/23/1995]
Could you please answer this math question? 34(67+789(47*79(243- 157)76-31)-85)48(34*423)-879) = ?

Concept of Factoring [03/22/1997]
Could you explain the concept of factoring and give examples of its practical uses?

Confusion over Interpretation of PEMDAS [03/24/2005]
Students take PEMDAS letter by letter, tending to do all multiplication before any division, rather than working from left to right. Here's a suggestion on how to help avoid that confusion.

Consecutive Integers [04/16/1997]
If the sum of two consecutive integers is less than one hundred, find the larger number.

Consecutive Integers Problem [2/16/1996]
Find three consecutive integers whose sum equals 66.

Consecutive Odd Integers [08/28/1997]
I need to know three consecutive odd integers that equal 150.

A Container Holds 5/8 Gallon... [11/05/1997]
If the container is 4/5 full and then 25 percent of the liquid is lost due to evaporation, how much liquid is left in the container?

Converting between Celsius and Fahrenheit [06/23/2009]
How can I use algebra to derive the unusual temperature conversion formulas F = 9/5(C + 40) - 40 and C = 5/9(F + 40) - 40 ?

Converting Seconds to MPH [07/11/2000]
I'm looking for a chart that converts the number of seconds needed to travel one mile to miles per hour.

Converting to an Equation [06/13/1999]
How can I convert "the square of a number is 96 more than 10 times the number" into an equation?

Correct Usage of Equal and Equivalent in Math Statements [02/20/2008]
Is there a mathematical difference between "equal" and "equivalent"?

Cost of a Ruler [08/01/1997]
Alice and Betty want to buy the same kind of ruler but Alice is 22 cents short and Betty is 3 cents short...

Cost of Pencils [6/26/1996]
Drawing pencils cost ... and coloured pencils cost... Two dozen assorted pencils cost $2.16. How many coloured pencils are there?

Cycling Digits [01/07/1998]
I have in mind a number which when you remove the units digit and place it at the front, gives the same result as multiplying the original number by 2...

Cycling Motion Problem [6/26/1996]
A cyclist travels from A to B over a high pass...

Cycling Uphill [7/8/1996]
I don't know how to handle the unknown speed at which the cyclist travels uphill.

Dealing with Duplicate Elements [05/17/2002]
I need to develop a general formula to calculate the number of different 'words' that can be formed from an N letter word where some of the letters may be duplicated.

Defining Counts [07/05/2016]
An adult struggles to disambiguate a unit label from the variable that represents the amount of that unit. Doctor Peterson clears up the confusion before reconciling the different uses with explicit labeling and dimensional analysis.

Definition of 'Solve' [11/29/2005]
In algebra class I was told that a problem such as 2 + 2 cannot be solved. In order to 'solve' a problem there has to be a variable involved. Is this correct?

Dependent and Independent Variables [12/26/2001]
Identify the dependent and independent variable: time it takes to travel 50 miles and the speed of the vehicle.

Deriving the Quadratic Formula [10/15/1998]
How do you derive the quadratic formula from ax^2 + bx + c = 0?

Difference in Radius, Difference in Speed [06/25/2002]
What is the difference in speed between a point on the tread of a tire and another point closer to the center, if the tire is rotating at 5000 rpm?

Difference of Squares of Two Integers [7/2/1996]
Which positive integers can be written as the difference of the squares of two integers?

Difference of Two Squares [08/17/1997]
Prove that every cube can be expressed as the difference of two squares.

The Difference of x and y... [06/05/2003]
The difference of a number and its square is 42. Is the equation x^2 - x = 42 or x - x^2 = 42?

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