312 CHAPTER 6 Algebra, Graphs, and Functions Brittany purchased a new battery for her SUV. Her total cost will include the price of the battery, 7% sales tax, and a battery recycling fee. The total cost that Brittany pays can be represented with an equation. When we use an equation to represent an application, we say that we are modeling the application using algebra. Throughout this section we will use algebra to model many real-life applications. Applications of Algebra SECTION 6.3 LEARNING GOALS Upon completion of this section, you will be able to: 7 Solve applications of linear equations in one variable. 7 Solve applications using proportions. Why This Is Important Being able to model real-life problems with algebra allows us to determine solutions to these problems. Some of the problems we will encounter in this section involve other financial applications as well as applications involving geometry, medicine, cooking, and traveling. Learning how to use algebra to solve application problems provides us with a powerful tool that can be used in many aspects of our lives. Applications of Linear Equations in One Variable One reason to study algebra is that it can be used to solve everyday problems. In this section, we will do two things: (1) show how to translate a written problem into a mathematical equation and (2) show how linear equations can be used in solving everyday problems. We begin by illustrating how English phrases can be written as mathematical expressions. When writing a mathematical expression, we may use any letter to represent the variable. In the following illustrations, we use the letter x. 60. Volume of an Ice-Cream Cone An ice-cream cone is filled with ice cream to the top of the cone. Determine the volume, in cubic inches, of ice cream in the cone if the cone’s radius is 1.5 in. and the height is 7 in. (See the figure.) The formula for the volume of a cone is V r h 1 3 . 2 π = 16.49 in.3 1.5 in. 7 in. Challenge Problem/Group Activity 61. Determine the volume of the block shown in Fig. 6.2, excluding the hole. The formula for the volume of a rectangular solid is V lwh. = The formula for the volume of a cylinder is V r h. 2 π = ≈ 1051.47 in.3 120 120 80 40 Figure 6.2 Serezniy/123RF
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