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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.

Quadratic Equation [6/22/1996]
What is a quadratic equation used for?

Quadratic Equation [8/28/1996]
What is the formula for the quadratic equation?

Quadratic Equation [04/08/1997]

Quadratic Equations [3/19/1996]
How are quadratic equations used in the real world?

Quadratic Equations [6/25/1996]

Quadratic Formula [5/11/1995]
Could you give me the quadratic formula?

Quadratic Formula, Distributive Property [06/02/1997]
Who invented the quadratic formula?

Quadratic Function: Definition [8/6/1996]
What is a "quadratic function"?

Quadrilateral Patterns [03/06/1997]
What is the formula that gives the number of quadrilaterals within a square grid when you increase the square grid by one unit on each side?

Questions about Zero - Undefined or Indeterminate? [8/16/1995]
Is 0,0,0,... a geometric sequence? What is the value of 0/0? What is the value of 0^0 (^ means exponent)? Can it be considered to be the limit of a^0 as a approaches 0?

Questions Answered Correctly [06/11/2003]
There are 30 multiple-choice questions in a contest. Five marks are awarded for each correct answer, and three marks are deducted for each incorrect answer. No marks are awarded for questions left unanswered. If a student scores 78 marks, what is the greatest possible number of questions answered correctly?

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?

Rates of Paddling [04/25/2000]
I can travel 12 miles downstream in six hours less than it takes me to travel the same distance upstream... How fast is this river's current?

Rationalizing the Denominator [05/27/1997]
Why do we have to rationalize the denominator?

Rational Number and its Reciprocal [03/14/2002]
A rational number greater than one and its reciprocal have a sum of 2 1/6. What is this number? Express your answer as an improper fraction in lowest terms.

Rational Root Theorem [08/27/1998]

Ratio of Anti-Freeze to Water [02/05/2003]
A barrel is filled with 45 gallons of anti-freeze. 9 gallons are removed and the barrel is refilled with water. 9 gallons of the mixture are removed and again, the barrel is refilled with water. What is the final ratio of anti-freeze to water in the barrel?

Ratio of Ratios [06/05/2002]

The Ratio of Water to Wine [10/22/1995]
A cask is filled with 45 gallons of wine. Nine gallons are removed and the cask is refilled with water. The nine gallons of the mixture are removed and the cask is again refilled with water. What is the ratio of water to wine in the final mixture?

Ratios and Mixtures [05/10/2001]
Sue needs to mix up a potion for her client... in what ratio must Sue mix the honey and turpentine?

Rearranging Variables [10/01/1998]



Relations versus Functions [10/27/1998]

Restrictions on Variables in Division [8/4/1996]
What are the restrictions on the variables in (y^3+8)/(y^2+3y+2)?

Reversing the Inequality [09/21/1998]
Why does the inequality sign reverse when you multiply by a negative number?

Reversing the Inequality Symbol [03/09/1999]

A Right Triangle of Points [01/14/1999]

Rule of Three [06/15/2002]
Please explain to me briefly (and with an example) the concept of the rule of three.

Rules of Exponent Manipulation [1/22/1996]
f sub r equals the reciprocal of ...



Same Day Off? [12/08/2002]

Savings on Gasoline [05/22/2001]

Scale Factor Acrobatics [07/15/2014]
A homeschooled teen struggles to make headway with a word problem in two unknowns. After emphasizing the scale factor in their ratio, Doctor Ian models the scenario algebraically.

Sets and Subsets [1/23/1995]


Shadow Game [01/28/2001]


Shortcut for Comparing Fractions [01/14/2003]
My teacher showed us how to cross multiply to compare fractions.


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