6.1 Order of Operations and Solving Linear Equations 305 57. + − = − − + − x x x x 3 2 6 15 8 5 −3 58. + − = + − + x x x x 6 822 2814 1012 − 5 21 59. + = − + n n n 4(3 1) 5(4 6) 9 2 60. − + = − t t 4( 3) 8 4(2 6) 5 61. + = x 1 2 1 3 2 3 2 3 62. + = y 1 2 1 3 1 4 − 1 6 63. + = x x 4 2 1 3 4 27 64. + = r r 3 2 7 3 65. x x 0.05 13.65 + = 13 66. x x 0.15 59.5 − = 70 67. + = − x x 0.2 1.3 0.4 4.5 29 68. − = + x x 3.01 5.2 2.91 1.57 67.7 69. − − − = − + x x x 7( 3) 4(2 1) 2( 4) 9 70. x x x 6(2 5) 4( 7) 3(3 2) − − + − = − − 4 71. + − = − x x 2( 3) 4 2( 4) No solution 72. + + − = − x x x 3( 2) 2( 1) 5 7 No solution 73. − + = − x x 4( 4) 12 4( 1) All real numbers 74. + − = − t t 6( 2) 14 6 2 All real numbers Problem Solving 75. Sales Tax If the sales tax rate on an item is 8%, the sales tax, t, on an item costing x dollars can be determined by the equation = t x 0.08 . Amina purchased a new set of air tags for $99 and paid 8% sales tax. a) Determine the amount of sales tax Amina paid when purchasing the air tags. $7.92 b) Determine the total amount, including sales tax, that Amina paid for the air tags. $106.92 c) Amina also purchased a case for her cell phone and paid 8% sales tax. If the sales tax paid on the case was $2.16, determine the price of the case prior to the sales tax. $27 76. Sales Tax If the sales tax rate on an item is 9.5%, the sales tax, t, on an item costing x dollars can be determined by the equation = t x 0.095 . Beau purchased a new smartwatch for $178 and paid 9.5% sales tax. a) Determine the amount of sales tax Beau paid when purchasing the smartwatch. $16.91 b) Determine the total amount, including sales tax, that Beau paid for the smartwatch. $194.91 c) Beau also purchased an additional smartwatch charger and paid 9.5% sales tax. If the sales tax paid on the charger was $1.14, determine the price of the charger prior to the sales tax. $12 $ $ 77. Moving Van Rental Costs The daily cost to rent a moving van is $75 plus 45 cents per mile the van is driven. The daily cost of renting the van, C, in dollars, can be represented with the equation, = + C x 75 0.45 , where x represents the number of miles that the van is driven. a) Determine the daily cost of renting the van if the van is driven 160 miles. $147 b) If the daily cost of renting the van was $168.60, how many miles was the van driven? 208 miles 78. Salary Plus Commission Alia works in a surf shop. She earns a weekly salary of $475 plus a commission of 15% of her weekly sales total. Alia’s weekly earnings, E, can be represented with the linear equation = + E x 475 0.15 , where x represents her weekly sales. $ $ a) Determine Alia’s weekly earnings if her weekly sales were $1500. $700 b) For one week, Alia’s weekly earnings were $649. Determine her weekly sales. $1160 79. Temperature Conversion Temperatures measured in degrees Celsius, C, can be converted to degrees Fahrenheit, F, using the equation = + F C 9 5 32. Use this equation to convert the following temperatures to degrees Fahrenheit. a) 0 C° (freezing temperature of water) 32 F° b) 100 C° (boiling temperature of water) 212 F° c) 35 C° (temperature of a summer day in Rio de Janeiro, Brazil) 95 F° d) −5 C° (temperature of a winter day in Toronto, Canada) 23 F° 80. Temperature Conversion Temperatures measured in degrees Fahrenheit, F, can be converted to degrees Celsius, C, using the equation C F 5 9 ( 32). = − Use this equation to convert the following temperatures to degrees Celsius. a) 32 F° (freezing temperature of water) 0 C° b) 212 F° (boiling temperature of water) 100 C° c) 104 F° (temperature of a summer day in Phoenix, AZ) 40 C° d) −13 F° (temperature of a winter day in Fairbanks, AK) −25 C° Fimina Anna/Shutterstock
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