WORD PROBLEMSAlgebraWORD PROBLEMSThis chapter covers ways of setting up word problems and solving forthe unknowns.EO 1.5 Given a word problem, write equations and SOLVE forthe unknown.BasicApproachtoSolvingAlgebraicWordProblemsAlgebra is used to solve problems in science, industry, business, and the home. Algebraicequations can be used to describe laws of motion, pressures of gases, electric circuits, and nuclearfacility operations. They can be applied to problems about the ages of people, the cost ofarticles, football scores, and other everyday matters. The basic approach to solving problems inthese apparently dissimilar fields is the same. First, condense the available information intoalgebraic equations, and, second, solve the equations. Of these two basic steps, the first isfrequently the most difficult to master because there are no clearly defined rules such as thosethat exist for solving equations.Algebraic word problems should not be read with the objective of immediately determining theanswer because only in the simpler problems is this possible. Word problems should be initiallyread to identify what answer is asked for and to determine which quantity or quantities, if known,will give this answer. All of these quantities are called the unknowns in the problem.Recognizing all of the unknowns and writing algebraic expressions to describe them is often themost difficult part of solving word problems. Quite often, it is possible to identify and expressthe unknowns in several different ways and still solve the problem. Just as often, it is possibleto identify and express the unknowns in several ways that appear different but are actually thesame relationship.In writing algebraic expressions for the various quantities given in word problems, it is helpfulto look for certain words that indicate mathematical operations. The words "sum" and "total"signify addition; the word "difference" signifies subtraction; the words "product," "times," and"multiples of" signify multiplication; the words "quotient," "divided by," "per," and "ratio" signifydivision; and the words "same as" and "equal to" signify equality. When quantities are connectedby these words and others like them, these quantities can be written as algebraic expressions.Sometimes you may want to write equations initially using words. For example, Bob is 30 yearsolder than Joe. Express Bob’s age in terms of Joe’s.Bob’s age = Joe’s age plus 30 yearsMA-02 Page 42 Rev. 0
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