318 CHAPTER 6 Algebra, Graphs, and Functions Example 6 Insulin Dosage Insulin comes in vials labeled with the number of insulin units per cubic centimeter (cc) of fluid. An insulin vial labeled U40 has 40 insulin units per cc of fluid. Tyler’s insulin dosage is 30 insulin units. How many cubic centimeters are needed for Tyler’s dosage? Solution The unknown quantity, x, is the number of cubic centimeters of fluid needed for Tyler’s dosage. Below is one proportion that can be used to determine that quantity. Given ratio { = = = = = x x x x 40 units 1 cc 30 units cc 40 30(1) 40 30 30 40 0.75 Tyler’s insulin dosage requires 0.75 cc of the fluid. 7 Now try Exercise 45 Exercises Warm Up Exercises In Exercises 1 and 2, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A quotient of two quantities is call a(n) _______. Ratio 2. A statement of equality between two ratios is called a(n) _______. Proportion Practice the Skills In Exercises 3–18, write the phrase as a mathematical expression. 3. 7 more than x x 7 + 4. 6 less than y y 6 − 5. The product of a b and ab 6. The quotient of c d and c d SECTION 6.3 Instructor Resources for Section 6.3 in MyLab Math • Objective-Level Videos 6.3 • Animation: Matching Verbal Statements to Equations • PowerPoint Lecture Slides 6.3 • MyLab Exercises and Assignments 6.3 Next, we solve for x by using cross multiplication. = = = ≈ x x x x (4.31)(12,451) 1000 53,663.81 1000 53,663.81 1000 1000 1000 53.66 The Chens’ cost for water in September is about $53.66. b) The unknown quantity in this problem is the number of gallons of water used in October. We let x the number of gallons used in October. = Then, we set up a proportion to solve this problem. The proportion we use is x x costof1000 gal 1000 gal 49.73 gal 4.31 1000 49.73 Given ration{ = = Note, unlike in part a), the unknown quantity is the number of gallons and therefore the x is in the denominator. Next, we solve for x by using cross multiplication. x x x 4.31 1000(49.73) 4.31 49,730 11,538.28 = = ≈ The Chens used approximately 11,538.28 gallons of water in October. 7 Now try Exercise 43
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