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.