A74 APPENDIX Review 21. Student Loan Wael took out a $12,000 loan to help pay for college. Part of the loan was borrowed at a rate of 4% per year and the rest at the rate of 5.5% per year. If the interest Wael paid at the end of the year totaled $600, how much was loaned at 4%? 22. Student Loan Aditi enrolled in a technical skills training program to become a professional welder. She borrowed $15,000 in a simple interest loan to pay for the program when she enrolled. She deferred payments for two years and owed $16,350 when she graduated. What was her interest rate? 23. Blending Teas The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 100 pounds of the new blend. The selling price of the new blend is to be $5.50 per pound, and there is to be no difference in revenue between selling the new blend and selling the other types. How many pounds of the Earl Grey tea and of the Orange Pekoe tea are required? 24. Business: Blending Coffee A coffee manufacturer wants to market a new blend of coffee that sells for $4.10 per pound by mixing two coffees that sell for $2.75 and $5 per pound, respectively.What amounts of each coffee should be blended to obtain the desired mixture? [Hint: Assume that the total weight of the desired blend is 100 pounds.] 25. Business: Mixing Nuts A nut store normally sells cashews for $9.00 per pound and almonds for $4.50 per pound. But at the end of the month the almonds had not sold well, so, in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for $7.75 per pound. How many pounds of cashews should be mixed with the almonds to ensure no change in the revenue? 26. Business: Mixing Candy A candy store sells boxes of candy containing caramels and cremes. Each box sells for $12.50 and holds 30 pieces of candy (all pieces are the same size). If the caramels cost $0.25 to produce and the cremes cost $0.45 to produce, how many of each should be in a box to yield a profit of $3? 27. Physics: Uniform Motion A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat travels upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? See the figure. 28. Physics: Uniform Motion A motorboat heads upstream on a river that has a current of 3 miles per hour.The trip upstream takes 5 hours, and the return trip takes 2.5 hours. What is the speed of the motorboat? (Assume that the boat maintains a constant speed relative to the water.) 29. Physics: Uniform Motion A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to find the speed of the current. 30. Physics: Uniform Motion Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 am, each heading for Wildwood. One car’s average speed is 10 miles per hour more than the other’s. The faster car arrives at Wildwood at 11:00 am, 1 2 hour before the other car. What was the average speed of each car? How far did each travel? 31. Moving Walkways The speed of a moving walkway is typically about 2.5 feet per second. Walking on such a moving walkway, it takes Karen a total of 48 seconds to travel 50 feet with the movement of the walkway and then back again against the movement of the walkway.What is Karen’s normal walking speed? Source: Answers.com 32. High-Speed Walkways Toronto’s Pearson International Airport has a high-speed version of a moving walkway. If Liam walks while riding this moving walkway, he can travel 280 meters in 60 seconds less time than if he stands still on the moving walkway. If Liam walks at a normal rate of 1.5 meters per second, what is the speed of the walkway? Source: Answers.com 33. Tennis A regulation doubles tennis court has an area of 2808 square feet. If it is 6 feet longer than twice its width, determine the dimensions of the court. Source: United States Tennis Association 34. Pickleball A regulation pickleball court has an area of 880 square feet. Its width is 2 feet less than half its length, determine the dimensions of the court. 35. Working Together on a Job Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they worked together? 36. Working Together on a Job Patrice, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms? 37. Enclosing a Garden A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. See the figure. (a) If the length of the garden is to be twice its width, what will be the dimensions of the garden? (b) What is the area of the garden? (c) If the length and width of the garden are to be the same, what will be the dimensions of the garden? (d) What will be the area of the square garden? 2 ft 2 ft 38. Construction A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long. (a) If the pond is square, what are its dimensions? (b) If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions? (c) If the pond is circular, what is its diameter? (d) Which pond has the larger area?
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