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Algebraic Word Problems
A lesson in Algebraic Expressions in Word Problems:
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Algebra word problems are very useful to solve real-life problems. You CAN do them. Remember the famous words of Albert Einstein

"Do not worry about your difficulties in mathematics, I assure you that mine are greater."

Background

When you take a real-world situation and translate it into math, you are actually 'expressing' it; hence the mathematical term 'expression'. Everything that is left of the equal sign is considered to be something you are expressing. Everything to the right of the equal sign (or inequality) is yet another expression. Simply stated, an espression is a combination of numbers, variables (letters) and operations. Expressions have numerical value. Equations are sometimes confused with expressions. To keep these two terms separate, simply ask yourself if you can answer with a true/false. If so, you have an equation, not an expression which would have numerical value. When simplifying equations, one often drops expressions such as 7-7 that equal 0.

A few samples:

Word Expression Algebraic Expression
x plus 5
10 times x
y - 12
x 5
5x
y - 12

Getting Started

Word problems consist of sentences. You will need to read the problem through carefully to ensure you have some understanding of what you are being asked to solve. Pay close attention to the problem to determine the key clues. Focus on the final question of the word problem. Read the problem again to make sure you understand what you're being asked for. Then, jot down the expression.

Let's get started:

1. On my last birthday I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?

a) x 125 b) 125 - x c) x 125 d) 125x

2. If you multiply the square of a number n by 6 and then added 3 to the product, the sum is equal to 57. One of the expressions equals 57, which one is it?

a) (6n)2 3 b) (n 3)2 c) 6(n2 3)d) 6n2 3

Answer for 1 is a) x 125

Answer for 2 is d) 6n2 3

On your own:

Sample 1:
The price of a new radio is p dollars. The radio is on sale for 30% off. What expression will you write that will tell the savings that is being offered on the radio?

Answer: 0.p3


Your friend Doug has given you the following algebraic expression: "Subtract 15 times a number n from twice the square of the number. What is the expression that your friend is saying?


Answer:
2b2-15b

Sample 3
Jane and her three college friends are going to be sharing the cost of a 3 bedroom apartment. The cost of rent is n dollars. What expression can you write that will tell yu what Jane's share is?


Answer:

n/5

Becoming quite familiar with the use of algebraic expressions is an important skill to learning Algebra!

Next Lesson: Expressions with more than one term.

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