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Word Problems

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

Selected answers to common questions:
    Solving simple linear equations.

Finding Speed, Distance, and Time [10/31/2002]
Time = distance/speed. Does this symbol (/) mean that distance divided by speed will give you time?

Find the Equation of the Tangent Line [1/21/1996]
Find the the equation of the tangent line when x=1....

Find the Numbers [08/28/2003]
One number is 61 more than a second number. The sum of the two numbers is 127. Find the numbers.

Formulas and Missing Quantities [10/09/2004]
Variations on the question "Could you drink enough water in a lifetime to empty a pool?" lead to a discussion of using formulas to find missing quantities.

Formulas for the Equation of a Line [09/28/1998]
Can you explain the meaning behind the point-slope formula? What about other formulas for the equation of a line?

Fractional Coefficients [1/21/1996]
x-4/8 - 5-2x/3 = 7/12 ?

General Strategies on Solving Linear Algebraic Equations [04/04/2005]
How do I solve equations like 12k + 15 = 35 + 2k? Is there a standard rule to follow?

Graphing Systems of Equations [06/01/1998]
How do you solve this system of equations by graphing: 3x + 2y = 5 and - 3x - 2y = 10?

How Far Did the Plane Fly? [01/23/2003]
A plane flew 440km/h to its destination. It then flew 500km/h back. If the whole trip took 9 hours, how far did the plane fly?

How Many Coins Did Each Originally Have? [10/22/2001]
Natalie has some nickels, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters... How many coins did each originally have?

How Many Mice, Cats, and Dogs? [01/13/2003]
You must spend $100 to buy 100 pets, choosing at least one of each pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and dogs @ $15.00 each. How many mice, cats, and dogs must you buy?

Interpreting Slopes [09/14/1998]
Does the graph of each of these equations rise to the right, fall to the right, is it horizontal, or is it vertical?

Introduction to Linear Equations and Slope/Intercept Form [03/19/2005]
I'm an 8th grader, and I was looking at linear equations in your algebra archives. I'm not sure what they are, so can you explain them to me in a way that I can understand?

Irrational Equations [06/02/2002]
I know what a rational equation is, but what's an irrational equation?

Isolating Groceries from Total Expenses, and Problems from Paragraphs [09/03/2011]
Given functions in a word problem, an adult student doesn't know how to begin subtracting one from the other. Before clarifying her use of variables, Doctor Peterson suggests reading through the problem strategically, to distill it down to just algebraic statements.

I Solved It. Now What? [10/16/2003]
I can solve an equation like 12 = 5x + x + 6 to get x = 1, but I don't know what it means, or what I'm supposed to do next.

Linear Equations in One Variable [10/11/2001]
Solve: 35 = 17 + 3(x-2).

Manipulating a Formula Algebraically [06/15/2006]
How do you solve M = C(1 + r) for r?

Missing Factors [01/29/1998]
I can not figure out how to find the two missing factors when given two equations.

Missing Terms [12/19/1994]
Find the missing terms: ?(?-3)=5w-15   I don't understand how you get the answer - what exactly is it looking for?

Mixture Problem [11/11/1997]
How much pure antifreeze should be added to 3 gallons of a 30 percent antifreeze solution to get 65 percent antifreeze?

More Variables Than Equations in a System [01/21/2002]
I have a problem that uses four variables but only two equations to relate them. I don't seem to have enough information to figure out the value of each variable or answer the question. Can you help?

A Mule and a Donkey [04/08/1999]
A famous Euclidean brainteaser.

Multiplying Fractions [1/9/1998]
What times 20 equals 16?

Multiplying or Dividing by a Negative Number [04/08/1999]
When x(x-4) is less than 0...

Nonsense Solutions to Word Problems [04/28/2003]
Bill, Simon, and John are brothers. Bill is as many years younger than one brother as he is older than the other. Simon is 7 years younger than twice the age of John. John is 5 years older than half the age of one of his brothers. I keep getting -3 for Simon's age. What am I doing wrong?

Order in Linear Expressions [11/20/2001]
Can you give me a convincing argument as to why, in an equation such as y=13-7x, where y is a function of x, it should be written as y=-7x+13?

Order of Operations and Solving Linear Equations [03/01/2006]
When solving an equation like 2x - 3 = 5, why do we add 3 first and then divide by 2? Why do equations not follow PEMDAS rules, which would suggest that we should divide before adding?

Parallel and Perpendicular Lines [01/14/1999]
How do you tell without graphing whether the graphs of these equations are parallel, perpendicular, or neither?

Plus or Minus Sign [03/08/2002]
What does this equation mean: y = +- k ? The - sign is directly under the + sign.

Population and Percentage [03/07/1999]
Given population data, find the number of women in two different years.

Pre-Algebra problem [11/11/1994]
How would you go about helping a typical 7th grade student with this problem? -3n + 65 = -40 - 7n

Probate Puzzle [12/15/2003]
A will specifies that every son should receive three times as much as a daughter and every daughter should get two times as much as their mother. What is the mother's share?

Quadratic Equation [04/08/1997]
The sum of two numbers is 15 and their product is 54. Find the numbers...

Quadratic Equation [7/10/1996]
Why is a quadratic equation "quadratic"?

Quadratic Equations [12/3/1995]
My students want to know why an equation of the second degree is referred to as a quadratic equation. What does the prefix quad have to do with second degree equations?

A Quadratic Word Problem [07/27/1999]
If the robbery rate per 1000 persons is increased by two and then decreased by 6, the product of the rate increased by 2 and the rate decreased by 6 is 180. What is the rate?

Raising Both Sides of an Inequality to a Power [06/19/2006]
You have to flip the sign in an inequality if you multiply both sides by a negative number. Is there any rule that says when you have to flip the sign if you raise both sides to a power?

Raising Sides of an Equation to the 0 Power [12/04/1997]
If you raise both sides of an equation to the 0 power, will both sides then be equal to one?

Rearranging an Equation [3/25/1996]
Rearrange the formula E=1/2mv to make v the subject.

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