18 Chapter 1Solving Linear Equations 45. COMPARING METHODS Solve the equation 2(4 8x) + 6 1 using (a) Method 1 from Example 3 and (b) Method 2 from Example 3. Which method do you prefer? Explain. 46. PROBLEM SOLVING An online ticket agency charges the amounts shown for basketball tickets. The total cost for an order is $220.70. How many tickets are purchased? ChargeAmountTicket price$32.50 per ticketConvenience charge$3.30 per ticketProcessing charge$5.90 per order47. MAKING AN ARGUMENT You have quarters and dimes that total $2.80. Your friend says it is possible that the number of quarters is 8 more than the number of dimes. Is your friend correct? Explain.48. THOUGHT PROVOKING You teach a math class and assign a weight to each component of the class. You determine  nal grades by totaling the products of the weights and the component scores. Choose values for the remaining weights and  nd the necessary score on the  nal exam for a student to earn an A (90%) in the class, if possible. Explain your reasoning.ComponentStudent’s scoreWeightScore WeightClass Participation92%0.2092% × 0.20 18.4%Homework95%Midterm Exam88%Final ExamTotal149. REASONING An even integer can be represented by the expression 2n, where n is any integer. Find three consecutive even integers that have a sum of 54. Explain your reasoning.50. HOW DO YOU SEE IT? The scatter plot shows the attendance for each meeting of a gaming club.Gaming Club Attendance Club AttendanceStudents0510152025yMeeting1234x182117a. The mean attendance for the  rst four meetings is 20. Is the number of students who attended the fourth meeting greater than or less than 20? Explain.b. Estimate the number of students who attended the fourth meeting.c. Describe a way you can check your estimate in part (b).REASONING In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x.51. bx 7 52. x + a 3 — 4 53. ax b 12.5 54. ax + b c55. 2bx bx 856. cx 4b 5bMaintaining Mathematical ProficiencyMaintaining Mathematical ProficiencySimplify the expression. (Skills Review Handbook) 57.4m + 5 3m 58. 9 8b + 6b 59. 6t + 3(1 2t) 5Determine whether (a) x = −1 or (b) x = 2 is a solution of the equation. (Skills Review Handbook) 60. x 8 9 61. x + 1.5 3.5 62. 2x 1 3 63. 3x + 4 1 64. x + 4 3x 65. 2(x 1) 1 3xReviewing what you learned in previous grades and lessons