26 CHAPTER 1 Critical Thinking Skills Learning Catalytics Keyword: Angel-SOM-1.3 (See Preface for additional details.) Many real-life problems, such as the one in Example 6, can be solved by using proportions. A proportion is a statement of equality between two ratios (or fractions). Proportions will be discussed in greater detail in Section 6.3. Example 5 Gas Mileage Davidson recently purchased a used hybrid SUV. Davidson fills his gas tank completely and writes down the odometer reading of 42,093.8 miles. The next time he stops for gas, it takes 12.3 gallons of gas to fill the tank and the odometer reading is 42,509.9 miles. a) Determine the gas mileage, in miles per gallon, that Davidson’s SUV got on this tank of gas. b) Assuming his gas mileage remains the same, determine the number of gallons of gas Davidson will need to drive to visit his sister and return home. The distance is 167.2 miles each way. c) If gas costs $3.47 pergallon, how much will Davidson pay for the gas needed for the trip? Solution Throughout this example, when necessary, we will round answers to the nearest hundredth. When rounding answers, we will use the symbol, ≈, which can be read as “approximately equal to.” a) We first determine the number of miles driven on the tank of gas by subtracting the smaller odometer reading from the larger odometer reading: − = 42,509.9 42,093.8 416.1 miles. Next, to determine the gas mileage, we divide the number of miles driven, 416.1 miles, by the number of gallons of gas, ÷ ≈ 12.3 gallons: 416.1 12.3 33.83 milespergallon. Thus, on this tank of gas, Davidson’s SUV got approximately 33.83 miles pergallon. b) We first determine the total number of miles driven. Since it is 167.2 miles each way, the total number of miles is 2 167.2 334.4 miles. × = Next, to determine the number of gallons of gas needed for this trip we divide the number of miles driven, 334.4 miles, by the gas mileage determined in part (a), 33.8 miles per gallon: ÷ ≈ 334.4 33.83 9.88 gallons. Thus, Davidson will need approximately 9.88 gallons of gas for his trip. c) To determine the cost of gas, we multiply the number of gallons needed for the trip, 9.88 gallons, by the price per gallon of gas, × $3.47 per gallon: 9.88 3.47≈ 34.28. Thus, the gas needed for the trip will cost Davidson approximately $34.28. 7 Now try Exercise 21 Example 6 A Brine Solution Some recipes for smoking a turkey recommend presoaking the turkey in a brine solution. To make enough brine solution to smoke a 12-pound turkey, use 16 tablespoons (tbsp) of salt in 2 gallons (gal) of water. a) If you wish to make 3.5 gallons of a brine solution, how much salt is needed? b) If you wish to make enough brine solution to soak a 20-pound turkey, how much salt is needed to make the brine solution? Solution a) To make 3.5 gallons of a brine solution, we need to determine how much salt is needed to mix with 3.5 gallons of water. To solve this problem, we use the information that 16 tablespoons of salt is to be mixed with 2 gallons of water. We can use this ratio to set up a proportion to solve for the unknown quantity. 16 tbsp 2 gal ? tbsp 3.5 gal = ⎧ ⎨ ⎩ Given ratio d Item to be found d Other information given
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