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324Chapter 5 Percent3. If 42% of the students in a certaincollege are female andthere are 3,360 female students,what is the total number of studentsin the college?Example 3If 48% of the students in a certain college are female andthere are 2,400 female students, what is the total number of students in thecollege?Solution We restate the problem as:There are 5,000 students.2,400 is 48% of what number?g g g g2,400 = 0.48 ⋅ ng​_2,4000.48 ​= ​​ _ 0.48​⋅ n​ Divide both sides by 0.48​ 0.48​n = ​_2,400 ​ Switch the left and right0.48sides of the equationn = 5,0004. Suppose in Example 4 that 35%of the students receive a gradeof A. How many of the 300 studentsis that?Example 4If 25% of the students in elementary algebra coursesreceive a grade of A, and there are 300 students enrolled in elementary algebrathis year, how many students will receive A’s?Solution After reading the question a few times, we find that it is the same asthis question:What number is 25% of 300?g g ggn = 0.25 ⋅ 300n = 75Thus, 75 students will receive A’s in elementary algebra.gAlmost all application problems involving percents can be restated as one ofthe three basic percent problems we listed in Section 5.2. It takes some practicebefore the restating of application problems becomes automatic. You may have toreview Section 5.2 and Examples 1–4 above several times before you can translateword problems into mathematical expressions yourself.Getting Ready for ClassAfter reading through the preceding section, respond in your ownwords and in complete sentences.1. On the test mentioned in Example 1, how many questions would thestudent have answered correctly if she answered 40% of the questionscorrectly?2. If the bottle in Example 2 contained 30 milliliters instead of 60, whatwould the answer be?3. In Example 3, how many of the students were male?4. How many of the students mentioned in Example 4 received a gradelower than A?Answers3. 8,000 students 4. 105 students