Percent - XYZ Custom Plus

Introduction . . .General Applications of PercentAs you know from watching television and reading the newspaper, we encounterpercents in many situations in everyday life. A recent newspaper article discussingthe effects of a cholesterol-lowering drug stated that the drug in question“lowered levels of LDL cholesterol by an average of 35%.” As we progress throughthis chapter, we will become more and more familiar with percent. As a result, wewill be better equipped to understand statements like the one above concerningcholesterol.In this section we continue our study of percent by doing more of the translationsthat were introduced in Section 5.2. The better you are at working the problemsin Section 5.2, the easier it will be for you to get started on the problems inthis section.AApplications Involving PercentExample 1On a 120-question test, a student answered 96 correctly.What percent of the problems did the student work correctly?Solution We have 96 correct answers out of a possible 120. The problem canbe restated as96 is what percent of 120?m8m8m8m888888888m88888888896 = n ⋅ 120​_96 ​= ​n_ ⋅ ​ 120​​ Divide both sides by 120120 ​ 120​n = ​_96 ​ Switch the left and right120sides of the equationn = 0.80 Divide 96 by 120= 80% Rewrite as a percent5.3ObjectivesA Solve application problemsinvolving percent.Practice Problems1. On a 150-question test, a studentanswered 114 correctly.What percent of the problemsdid the student work correctly?Instructor NoteAs you can see, the key to thismethod of solving application problemsis to translate the problem intoone of the three basic percent questionsfrom the previous section.When we write a test score as a percent, we are comparing the original score toan equivalent score on a 100-question test. That is, 96 correct out of 120 is thesame as 80 correct out of 100.Example 2How much HCl (hydrochloric acid) is in a 60-milliliter bottlethat is marked 80% HCl?Solution If the bottle is marked 80% HCl, that means 80% of the solution isHCl and the rest is water. Because the bottle contains 60 milliliters, we can restatethe question as:2. How much HCl is in a40-milliliter bottle that ismarked 75% HCl?What is 80% of 60?gn = 0.80 ⋅ 60g ggn = 48gHCL 80%60 mlThere are 48 milliliters of HCl in 60 milliliters of 80% HCl solution.5.3 General Applications of PercentAnswers1. 76% 2. 30 milliliters323