320 CHAPTER 6 Algebra, Graphs, and Functions 41. MODELING—Enclosing Two Pens Chuck has 140 ft of fencing with which he wants to fence in two connecting, adjacent square pens with fencing between the two pens as shown in the following diagram. What will be the dimensions if the length of the entire enclosed region is to be twice the width? w w 3 2(2 ) 140; + = width:20ft, length:40ft l w 42. MODELING—Chicken Yard Rodney has 84 feet of fencing with which to build 3 separate pens for his chickens. The pens will be adjacent to the chicken coop as shown in the following diagram. Chicken Coop x x x x x x x The square pens are all the same size and will consist of fencing on only 3 sides with the coop on the remaining side. Determine the dimensions of each pen. x7 84;. = length 12 feet, width 12 feet In Exercises 43–50, use proportions to solve the problem. 43. Water Bill The water rate in Aurora, Colorado, is $5.87 per 1000 gallons of water used. a) During May, the Hindermans used 4327 gallons of water. Determine their water bill for May. $25.40 b) During June, the Hindermans had a water bill of $28.71. Determine the amount of water they used in June. 4890.97 gallons 44. Paint One gallon of paint covers a surface area of 350 ft .2 a) Assuming paint can only be purchased in whole gallons, how many gallons are needed to paint a house with a surface area of 6600 ft ? 2 19 gal b) While cleaning out his basement, Allen discovered that he has 3.5 gallons of paint. How many square feet of surface area will this amount of paint cover? 1225 ft2 Amount of Insulin In Exercises 45 and 46, how much insulin (in cc) would be given for the following doses? Refer to Example 6. 45. 35 units of insulin from a vial marked U40 0.875 cc 46. 15 units of insulin from a vial marked U40 0.375 cc $ 47. Topsoil A 40-pound bag of topsoil will cover a surface area of 12 ft .2 a) How many pounds of topsoil are needed to cover a surface area of 480 ft ? 2 1600 lb b) How many bags of topsoil must be purchased to cover a surface area of 480 ft ? 2 40 bags 48. Lasagna A recipe for 6 servings of lasagna uses 16 ounces of Italian sausage. a) If the recipe were to be made for 15 servings, how many ounces of Italian sausage would be needed? 40 ounces b) How many servings of lasagna can be made with 24 ounces of Italian sausage? 9 servings 49. The Proper Dosage A doctor asks a nurse to give a patient 250 milligrams (mg) of the drug simethicone. The drug is available only in a solution whose concentration is 40 mg simethicone per 0.6 milliliter (m ) of solution. How many milliliters of solution should the nurse give the patient? 3.75 m 50. Speed Limit When Jacob crossed over from Niagara Falls, New York, to Niagara Falls, Canada, he saw a sign that said 50 miles per hour (mph) is equal to 80 kilometers per hour (kph). m Niagara Falls a) How many kilometers per hour are equal to 1 mph? 1.6 kph b) On a stretch of the Queen Elizabeth Way, the speed limit is 90 kph. What is the speed limit in miles per hour? 56.25 mph Challenge Problems/Group Activities 51. Hotel Fees and Taxes While staying one night at a hotel, in addition to her room fee, Rhiannon also paid a $24 parking fee. The 7.5% sales tax applied to the room fee and to the parking fee. An additional 5% hotel tax applied only to the room fee. Rhiannon’s total amount owed, including room fee, parking fee, sales tax, and hotel tax was $348.68. Determine the room fee to the nearest cent. $287.00 52. Income Tax Some states allow spouses to file individual tax returns even though they have filed a joint federal tax return. It is usually to the taxpayers’ advantage to do so when both spouses work. The smallest amount of tax owed (or the largest refund) will occur when the spouses taxable incomes are the same. $ $ Olesya Baron/Shutterstock
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