Section 3.5 Applications and Problem Solving 167 51. The cost of a new car is about 5 times the cost of the same model that is ten years old. If x represents the cost of the ten-year-old car, write an expression for the cost of a new car. Minneapolis Madison Chicago x 120 x 52. Jacob scored four times as many points in his hockey game on Monday as he did in Wednesday’s game. If p represents the number of points scored on Wednesday, write an expression for the number scored on Monday. For Exercises 53–64, use the problem-solving flowchart to set up and solve an equation to solve each problem. 53. Felicia has an 8-ft piece of ribbon. She wants to cut the ribbon into two pieces so that one piece is three times the length of the other. Find the length of each piece. (See Example 5.) 54. Richard and Linda enjoy visiting Hilton Head Island, South Carolina.The distance from their home to Hilton Head is 954 mi, so the drive takes them 2 days. Richard and Linda travel twice as far the first day as they do the second. How many miles do they travel each day? 55. A motorist drives from Minneapolis, Minnesota, to Madison,Wisconsin, and then on to Chicago, Illinois. The total distance is 360 mi. The distance between Minneapolis and Madison is 120 mi more than the distance from Madison to Chicago. Find the distance between Minneapolis and Madison. 56. Two hikers on the Appalachian Trail hike from Hawk Mountain to Gooch Mountain. The next day, they hike from Gooch Mountain to Woods Hole. The total distance is 19 mi. If the distance between Gooch Mountain and Woods Hole is 5 mi more than the distance from Hawk Mountain to Gooch Mountain, find the distance they hiked each day. Woods Hole Gooch Mountain Hawk Mountain 57. The Beatles had 9 more number one albums than Elvis Presley. Together, they had a total of 29 number one albums. How many number one albums did each have? (See Example 6.) 58. A two-piece set of luggage costs $150. If sold individually, the larger bag costs $40 more than the smaller bag.What are the individual costs for each bag? 59. In a football game, the New England Patriots scored 3 points less than the New York Giants. A total of 31 points was scored in the game. How many points did each team score? 60. The most goals scored in a regular season NHL hockey game occurred during a game between the Edmonton Oilers and the Chicago Black Hawks. The total number of goals scored was 21. The Oilers scored 3 more goals than the Black Hawks. How many goals did each team score? 61. An apartment complex charges a refundable security deposit when renting an apartment. The deposit is $350 less than the monthly rent. If Charlene paid a total of $950 for her first month’s rent and security deposit, how much is her monthly rent? How much is the security deposit? 62. Becca paid a total of $695 for tuition and lab fees for fall semester. Tuition for her courses cost $605 more than lab fees. How much did her tuition cost? What was the cost of the lab fees? 63. Stefan is paid a salary of $480 a week at his job. When he works overtime, he receives $18 an hour. If his weekly paycheck came to $588, how many hours of overtime did he put in that week? 64. Mercedes is paid a salary of $480 a week at her job. She worked 8 hr of overtime during the holidays and her weekly paycheck came to $672.What is her overtime pay per hour?
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