Ask Dr. Math

Middle School Archive

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.

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Mixing Alcohol, Cable TV Pricing [8/2/1996]

What amounts of 9 percent and 12 percent alcohol do you mix to get 300,000 gallons of 10 percent alcohol? For each 5-cent increase in the monthly subscription price, 4 people will decide not to subscribe to cable TV...

Mixing Milk and Butterfat [09/04/2001]

Milk that has 5% butterfat is mixed with milk that has 2% butterfat. How much of each is needed to obtain 60 gallons of milk that has 3% butterfat?

Monomials and Polynomials [8/31/1995]

I really don't understand monomials and polynomials. Could you help explain them simply?

Monomials, Polynomials [01/21/1998]

I'm having trouble adding, subtracting, multiplying and dividing monomials, adding and subtracting polynomials, and factoring.

Multiples of 9 Number Puzzle [03/23/2003]

If you take a two-digit number, add the digits, and subtract the sum from the original number, why is the answer always a multiple of 9?

Negative Numbers in Equations [11/20/2001]

I don't know how to do some of the homework I am getting. Here are some examples of confusing equations: -30 = -37+b/15; -c/4-8 = -48.

No Solution, Infinite Solutions [01/03/2002]

Solve: 8(2x-3) = 4(4x-8); -3(x-3) is greater than or equal to 5-3x.

Number of Quarters [9/11/1996]

Tony has eleven more nickels than quarters. How many quarters does he have if the total value of his coins is $2.65?

Number Puzzle Solved with and without Algebra [12/10/2001]

I am a number. Add 25 to me. Divide the sum by 2. You end with 75. What number am I?

Order of Operations [8/21/1995]

What is the reason for the order of operations in a math equation?

Order of Operations: Math vs. English; Calculators [11/13/1996]

What is 144 divided by 3(8+4)? 4 or 576?

Order of Operations Puzzle [09/22/2002]

What is _ + _ x _ - _ = 22? We're given the numbers 2, 3, 4, 8.

Pre-Algebra: Equations and Other Tips [08/30/1997]

I'm in 8th Grade; can you give me tips on equations and other things that will be useful for me to know?

Pre-algebra variable expressions [09/01/99]

Please explain how to do variable expression problems.

Properties of Algebra [5/8/1996]

What are the properties used for algebra?

Properties of Exponents [01/22/2001]

Will you please help me understand exponents?

Properties of Real Numbers [05/20/1997]

What are the associative, the commutative, and the zero product properties?

Purpose of Algebra [10/15/1996]

What is the purpose of algebra and who came up with the idea?

Pythagorean Theorem Proof: Four Right Triangles [10/7/1996]

I don't understand the Pythagorean Theorem.

Real and Complex Equations [09/21/1998]

I'm having trouble simplifying some real and complex equations for Algebra II. Can you help?

Renting Bike Safety Equipment [10/09/2001]

The Park Department rents a bike with safety equipment for $5 a day. If you provide your own safety equipment, the bike rental is $3 a day. You could buy equipment at a sports store for $28. How many times must you use the trail to justify buying your own safety equipment?

Representing Numbers in Different Bases [08/05/1998]

How did they get the 2 x 3 cubed? Plus some number less than 3 cubed?...

Ruth Has $2300 More Than Ken [04/15/1999]

...If Ken gives Ruth $2000, Ruth will have eight times as much money as Ken. How much money does each of them have?

Silver Alloy [07/12/2001]

Sterling Silver is 92.5% pure silver. How many grams of pure silver and sterling silver must be mixed to obtain 100g of a 94% Silver alloy?

A Simple Formula? [02/21/1997]

If one person takes two hours to paint a wall and another only one hour, how long will it take them to paint the wall together?

Simplifying an Algebraic Expression [8/17/1996]

If 12y = 3, what do you do next?

Sketch an Equation [10/07/1997]

How do I rearrange -3x+2y = -6 to sketch it?

Solving Algebra Word Problems [10/16/1998]

I'm having trouble solving word problems. In particular, how do you convert the words to variables and then make them into equations?

Solving an Equation with Fractions [11/27/1995]

A student asks how to work the problem: (x + 5)/4 = (x-4)/(2/5).

Solving Another Equation with Two Variables [1/30/1996]

6y = 3D = 54. I am supposed to solve the equation, but I don't even understand it!

Solving ax + b is less than cx + d [12/11/2001]

Here is an inequality problem: 6-9x is less than or equal to 5x-1.

Solving Equations [01/25/1997]

How do you solve equations like n/4 + 6 = -3?

Solving Equations in Two Variables by Addition/Subtraction [09/08/2001]

The equations are: 2x + 3y = 7; 4x - 5y = 25.

Solving for X [8/14/1996]

Solve: (x/7) - 4 = -2.

Solving for x [10/22/1996]

How do you solve an equation like x/a = k for x?

Solving Quadratic Equations [5/23/1996]

5x+x(x-7)= 0

Solving Simple One-Variable Equations [02/14/1998]

n+39 = 12, w+(-8) = -21, 24 = m-8.6 ... I need help on these problems.

Solving Systems of Equations by Substitution [08/24/1998]

When they want you to substitute the x value in place of it in the y problem I totally get lost.

Substituting in Linear Equations [11/14/2001]

I am given two equations, 2y = 5x + 8x and 3y = 4x + 9x, and told to substitute something. What should I do?

Substitution and Elimination [01/13/2002]

Could you please explain substitution and elimination to me step by step?

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