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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.

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.

Rearranging an Equation [05/01/1999]
Solve for x in terms of y: y = (900x)/(2+x).

The Secret to Mathematics? [09/27/2004]
I understand how to divide fractions--invert and multiply--but what if the dividend or divisor is a variable?

Setting Up Algebraic Word Problems [08/04/2003]
If each photocopy of a manuscript costs 4 cents per page, what is the cost, in cents, to reproduce x copies of an x-page manuscript?

Setting up an Equation [05/25/1999]
When I add 4 to a number I get the same result as halving the number and adding 10. What is the number?

Setting Up Equations [11/26/1997]
An airplane travels eight times as fast as a car. The difference in their speeds is 420 km/h. How fast is each vehicle travelling?

Simple Equation: 3y + 2 over 4 equals 7 [10/17/2001]
I think you have to subtract 2 on both sides, but I'm lost.

Simplify and Solve [01/15/1998]
Simplify one side of the equation. Then solve. .75y + y + 10 = 45

Simplifying Answers [12/17/1994]
How do you answer questions like this? (p^2q^-4)^2 (p^3q^5)^- 3

Simplifying Expressions [11/24/1997]
Solve: 2x - ( 3 - x ) = x - 7 .

Simultaneous Equations [07/01/2002]
A man has a total of 20 dimes and quarters. If the dimes were quarters and the quarters were dimes he would have 90 cents more than he has now. How many of each coin does he have?

Solutions to Equations [01/16/1997]
How do you make a table of values of x and y that make the equation 3/4y = -x true?

Solve for X [10/09/1999]
How can I solve equations like 4x - (1/2) = -3/2?

Solving a Linear Equation in One Variable [02/27/1998]
Solve for q: -13 - q - 9 = 5q - 9 - q.

Solving an Equation with Decimals [1/31/1996]
I can't figure out what 15.6 + z = 20.4 is. I need step-by-step help.

Solving an Equation with Fractions [1/30/1996]
v = 6 - 5/4 v. I don't know if this question is asking 6 minus 1 1/4 or 6 * 1 1/4.

Solving another Equation in One Variable [1/12/1996]
-2[3-2(x-1) + 5(2-x)] = -3[x+2(x-1)]

Solving a System of Three Equations in Three Variables [06/23/2007]
How can I find values of x, y, and z that make all three of these equations true: x + y + z = 10, x - 2y + z = -2, and x - y - z = -12?

Solving Basic Equations with Variables [11/28/2004]
How do I solve an equation like 8x + 6 = 3x + 21?

Solving Equations [6/28/1996]
Solving Systems of Equations: find k, if 7/x+y = k/x+2 = 11/2-y

Solving Equations with Fractions in Them [12/06/2004]
How do you solve an equation like -5/7 n = 35?

Solving Equations with Square Roots [03/28/2003]
When solving x + 1 = sqrt(x + 3), we can square both sides then solve the equation; however, we get an extra solution that doesn't work. Why?

Solving for a Variable in One Equation [3/18/1996]
I need to write the following in standard form and solve for the indicated variable: (2r+3)(2r-1) = -(3r+1)

Solving for One Uknown among Many: How and Why [09/20/2010]
A student wonders how to solve for an unknown that appears in the middle of several others. Over the course of several back-and-forths with many examples, Doctor Ian reveals the different scopes of what it means "to solve," introduces the concept of sets of solutions, explains why you might want to isolate one term with respect to others, shows how to do so, decodes the meaning of a string of variables -- and reaffirms that, indeed, all the rules that the student has learned still work no matter the symbols.

Solving for One Variable of Many [05/30/2002]
How do you solve a formula with many variables for one of them?

Solving Linear Equations and the Scale Metaphor [08/26/2004]
When solving linear equations, why do we have to do the same operation on both sides of the equal sign?

Solving Linear Equations by Using Inverses [08/13/2003]
Solve for a in b = 5/7(a-8).

Solving Pairs of Equations by Substitution [11/26/1997]
x + 3y = - 5; 3x - 2y = 7.

Solving Problems With and Without Algebra [05/14/2002]
In a basketball game, Harold and Isaac scored a total of 19 points. Isaac and Jacob scored a total of 14 points. Isaac scored as many ponts as Harold and Jacob together. How many points did each player score? And how can I solve this without algebra?

Solving Simple Equations [02/23/1998]
Equations like 3(30+s) = 4(s+19) and others following the same form.

Solving Systems of Linear Equations [02/09/1999]
Can you help me solve simultaneous equations?

Solving Two Equations with Mixed Fractions [05/13/1998]
Steps to solving (2 2/3)x - 1 1/4 = 4 1/3 and (4 1/5)x - 2 = 3 1/3.

Splitting Peanuts [08/03/2002]
On a camping trip, the family had brought many bags of peanuts for snacks...

Step-by-step Solution of Equation in One Variable [05/13/1998]
Commutative, associative, distributive, and other laws of arithmetic applied to solve w in the equation 2 - 2(w + 6) = 2(w + 5).

Straight Line on the Graph [09/10/1998]
Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of y = ln(f(x)) is a straight line.

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