Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Concept Check - Page 133: 27

Answer

$1.$ Identify the Variable $2.$ Translate from Words to Algebra $3.$ Set up the Model $4.$ Solve the Equation and Check your Answer

Work Step by Step

Guidelines for modeling with equations consist of $4$ main steps. In the chapter $1.7$ of the textbook we read the following guidelines for modeling with equations: $1.$ Identify the Variable Identify the quantity that the problem asks you to find. This quantity can usually be determined by a careful reading of the question that is posed at the end of the problem. Then introduce notation for the variable (call it $x$ or some other letter). In short, a variable is an unknown value. $2.$ Translate from Words to Algebra Read each sentence in the problem again, and express all the quantities mentioned in the problem in terms of the variable you defined in Step $1$. To organize this information, it is sometimes helpful to draw a diagram or make a table. The way of doing this step can vary based on one's understanding in the topic. One way can be easy for someone and hard for other and vice versa. $3.$ Set up the Model Find the crucial fact in the problem that gives a relationship between the expressions you listed in Step $2$. Set up an equation (or model) that expresses this relationship. In short, we have to determine how one value affects another; how they are related to each other. $4.$ Solve the Equation and Check your Answer Solve the equation, check your answer, and express it as a sentence that answers the question posed in the problem.
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