Survey of Mathematics

10.1 Percent 589 Did You Know? Tipping The practice of tipping began in European coffeehouses in the eighteenth century. After the Civil War, wealthy Americans who traveled to Europe brought the custom back to the United States. Initially the custom was vehemently opposed by many groups. In 1897 the New York Times claimed that tipping is “antithetical to American democratic ideals.” Eventually the practice did catch on, and today many websites and apps are devoted to tipping guidelines for persons who work in a wide variety of occupations. For example, in the United States, it is customary to tip waiters and waitresses 15–20% of the pretax restaurant bill. Hairstylists should be tipped 15% of the bill, and pizza delivery persons should receive $1–$5 per pizza, depending on the distance driven. For other suggestions on the appropriate amount to tip for various services, see the Original Tipping Page: Tipping.org. Percent Markup or Markdown Percent markup (or markdown) on cost selling price dealer’s cost dealer’s cost 100% = − × Example 7 Determining Percent Markup Holdren Hardware stores pay $48.76 for wheelbarrows. They regularly sell them for $79.88. At a sale they sell them for $69.99. Determine a) the percent markup on the regular price. b) the percent markup on the sale price. Solution a) We determine the percent markup on the regular price as follows. Percent markup selling price dealer’s cost dealer’s cost 100% 79.88 48.76 48.76 100% 0.6382 100% 63.8% = − × = − × ≈ × ≈ Thus, the percent markup on the regular price was about 63.8%. b) We determine the percent markup on the sale price as follows. Percent markup 69.99 48.76 48.76 100% 0.4354 100% 43.5% = − × ≈ × ≈ Thus, the percent markup on the sale price was about 43.5%. 7 Now try Exercise 65 Example 8 Determining Percent Markdown To help reduce the inventory of its remaining calendars, Walgreens reduces the selling price to $4.00. If Walgreens cost per calendar was $5.00, determine the percent markdown on the calendars. Solution We will use the same formula that we used for percent markup in Example 7. Percent markdown selling price dealer’s cost dealer’s cost 100% 4.00 5.00 5.00 100% 0.20 100% 20% = − × = − × = − × = − Thus, the percent markdown on the calendars was 20%. 7 Now try Exercise 67 Other Percent Problems In daily life, we may need to know how to solve any one of the following three types of problems involving percent: 1. What is a 15% tip on a restaurant bill of $45.71? The problem can be restated as 15% of $45.71 is what number? Brezzell /Shutterstock

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