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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.

Subtracting One Equation from Another [05/30/2001]
Why can you subtract one equation from another and get something meaningful that you can use to solve the equations?

The Sum of Two Numbers is 20... [11/03/1997]
Twice one number is 4 more than four times the other. Find the numbers.

Switching Dollars and Cents [10/07/1997]
How do I find an equation?

System Of Equations With Products Of Variables [10/29/2003]
I'm trying to solve a system of three equations and three variables where the variables are multiplied together, such as 'xy' and 'yz'. Substitution doesn't seem to be working very well - what's a good way to get started?

Three Simultaneous Equations [4/16/1996]
Can you help me solve this problem?

To Multiply or Divide? That Is the Question. [09/02/2003]
In a story problem, how do you know whether to multiply or divide?

Trains, Times, and Tunnel Vision: Thinking beyond Formulas [06/28/2010]
A student seeks a formula to solve a "two trains" word problem. Rather than indulge in formulaic thinking, Doctor Ian suggests using related rates to make the problem simpler.

Transposing Equations [07/14/1998]
I am having trouble when transposing. When y = 2x + 3, how do you find the value of x?

Turning an Equation Upside-Down [07/09/2001]
After this step: 2/h = (a+b)/ab, a book shows this: h/2 = (ab)/(a+b). Can you simply invert the fractions and maintain the equivalency?

Two Planes and Not Enough Information [08/10/2004]
Two planes leave Chicago, one traveling due east and the other due west. The first travels 100 miles per hour faster than the second. How long will it be until they are 2000 miles apart?

Two Step Equations [02/24/1998]
How to solve two-step equations.

Two-Step Equations [01/30/2003]
What are two different two-step equations that have 1.2 as their solution?

Undefined Fractions [06/10/2005]
I am having trouble determining the difference between an undefined fraction and a fraction with no solution. Maybe you can help me determine the difference.

Understanding Parabolas [02/04/1997]
Explain why the sign of the x^2 coefficient in the equation for a parabola determines whether the parabola opens up or down?

Variables, Explained [05/05/2003]
I have problems trying to understand how to answer and work out these types of math problems: 13.7b - 6.5 = -2.3b + 8.3.

Variation on Combined Work [06/13/2002]
If you run a large pipe for 4 hours, and run a small pipe for 9 hours, you can fill 1/2 a pool. If you run both pipes together for 12 hours, you can fill the whole pool. How long would it take to fill the pool using each pipe by itself?

Writing Out Equations [12/18/1997]
How do you do equations like 6x+7 = 3x+16 ?

x - 8 = -5 [06/13/2001]
I know the answer but our teacher wants us to show all of our work and add something to both sides.

X- and Y-Intercepts [09/15/1998]
I'm having a hard time finding out how to solve an equation and then do the graph. The intercepts confuse me also...

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