Algebra word problems

Many algebra word problems involve a single number and some operations performed on it. The problems of this sort are good for practice in writing algebraic equations, because you only need to worry about one unknown, or variable. For simplicity, I ll use x for the unknown. 

Before getting into some serious algebra word problems, here are a few warm-ups to get you in the mood. 

Hinsley, D., Hayes, J., 8c Simon, H. (1977). From words to equations Meaning and representation in algebra word problems. In M. Just 8c P. Carpenter (Eds.), Cognitive processes in comprehension (pp. 89-106). Hillsdale, NJ Lawrence Erlbaum Associates. 

The following section consists of 10 sets of miscellaneous math, including basic arithmetic questions and word problems with whole numbers. You will also see problems involving pre-algebra concepts such as negative numbers, exponents, and square roots (getting you ready for the algebra in Section 5). This section will provide a warm-up session before you move on to more difficult kinds of problems. 

The math word problems in this book span some basic problems (using arithmetic) to the more complex (requiring algebraic skills). Even though I like to make example problems come out with whole-number answers, sometimes... 

Part 111 Tackling Word Problems from Algebra... 

A math word problem is full of words — big surprise Word problems really represent the real world. When you have a problem to solve at the office involving ordering new file cabinets, you don t sit down to write out your times tables, and you aren t handed a piece of paper with an algebra problem asking you to solve 2x + 3 = 27. To be successful with a word problem, you... 

A math word problem is different from other arithmetic and algebra problems, because you first have to translate from the words to the symbols before you do the operations or solve the equation for the answer. 

The translations from word problems to algebraic problems have two standard rules ... 

You get that feeling of satisfaction when an algebraic equation or inequality works out and you get one or more solutions. The next step in word problems is then, of course, to see if the solution of the equation or inequality is an answer to the problem. If the solution doesn t work, then you go back to see if you ve done some miscomputation. But sometimes, no amount of good mathematics is going to get you an answer. It could be that the question just doesn t have an answer. 

Traditional age word problems use algebraic expressions to write comparisons such as twice the age of or four years older than and then solve for one or more person s age. You ll see lots of parentheses in the equations that are first written so that the meaning is clearly defined and the people s ages are clearly identified. Age problems can get pretty wordy and confusing, so you want to be sure that you ve written something to parallel the wording. 

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