1.3 Problem-Solving Procedures 25 information on converting percents to decimal numbers, see Section 10.1. Next, multiply the decimal number, 0.065, by the amount, $28.00. Sales tax 6 % of 28.00 0.065(28.00) 1.82 1 2 = = = The sales tax is $1.82. The total bill is the cost of the meal + the sales tax. Total bill cost of meal sales tax 28.00 1.82 29.82 = + = + = Thus, the bill, including sales tax, is $29.82. b) To determine 15% of any number, we can multiply the number by 0.15. 15% of pretax cost 0.15($28.00) $4.20 = = Thus, 15% of $28.00 is $4.20. A second method to determine a 15% tip is to determine 10% of the cost and then add to it half that amount. Following this procedure, 10% of pretax cost 0.10($28.00) $2.80 = = Now add half of $2.80 to $2.80. $2.80 $2.80 2 $2.80 $1.40 $4.20 + = + = c) To determine 20% of any number, we can multiply the number by 0.20. 20% of pretax cost 0.20($28.00) $5.60 = = Thus, 20% of $28.00 is $5.60. A second method to determine a 20% tip is to determine 10% of the cost, as we showed in part (b), and then double this amount. 10% of pretax cost 2 $2.80 2 $5.60 × = × = Tips are often rounded to the nearest dollar. For more information, there are many websites dedicated to the tipping process. 7 Now try Exercise 25 TECHNOLOGY TIP There’s an App for That! Throughout this book we will be discussing many different applications of mathematics. Many of the applications can be further explored with the use of an app on your smartphone or tablet. For example, in Example 4, we discussed calculating a tip based on the cost of a meal. There are many apps that can assist you in calculating tips at restaurants, hair salons, golf courses, airports, and other places where tipping is customary. Furthermore, if you travel to other countries, these apps can assist you in determining an appropriate tip for these locations. Within Technology Tip boxes, we will discuss many useful apps throughout this book. You may already be aware of some of these apps. However, always consult with your instructor before using these apps when completing work related to your course. MATHEMATICS TODAY Decisions, Decisions We deal with problem solving daily. Can we afford to take a family trip to a theme park? Which vehicle should I purchase? What shall I major in in college? The list of questions we ask ourselves daily goes on and on. To make decisions, we often need to consider and weigh many factors. Often, different branches of mathematics are involved in our decision-making process. For example, we frequently use statistical data and consider the probability (or chance) of an event occurring or not occurring when we make decisions. Probability and statistics are two branches of mathematics covered in later chapters of the book. For many people, problem solving is a recreational activity, as is evident by the great number of crossword puzzles and puzzle books sold daily. Today, as you go about your daily business, keep a record of all the problem-solving decisions you need to make! If you do this conscientiously, you will be amazed at the outcome. Why This Is Important There are aspects of problem solving to almost every decision we make. Kali9/E+/Getty Images Rido/Shutterstock
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