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Word problem.

In science education, a word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.[1] As word problems often involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used.[2]

Example

The most common types of word problems in elementary algebra are distance problems, age problems, work problems, percentage problems, mixtures problems and numbers problems.

A typical age problem:

Ann is three times as old as her little brother Bob. In five years, she will be only twice as old. How old are they now?

To solve this by algebra, one first translates the words into mathematical variables, operations, and equations:

• Write Ann’s age as the variable A, and Bob’s age as B.

• Their ages five years from now are A+5 and B+5.

• Twice as old means one age equals two times another, and similarly for three times.

The problem thus becomes:

Solve the system of equations A = 3B and A+5 = 2(B+5) for variables A,B.

The answer is A = 15, B = 5, or in ordinary language: Ann is fifteen years old, and Bob is five.

Structure

Word problems such as the above can be examined on three levels:

• A. The verbal formulation;

• B. The underlying mathematical relations;

• C. The symbolic mathematical expression.

Linguistic properties can include such metrics as the number of words in the problem or the mean sentence length.[4] One scheme to analyze the logico-mathematical properties is to classify the numerical quantities in the problem into known quantities (values given in the text), wanted quantities (values to be found) and auxiliary quantities (values found as intermediate stages of the problem).