Section 2.6 Percent, Rate, and Mixture Problems 165 62. Joan has a collection of dimes and nickels. She has 38 fewer dimes than nickels. If the collection is worth $7, how many dimes and nickels does she have? 63. A sweater is on sale for $20.35. If this price is 45% off the original price, what is the original price of the sweater? 64. A jacket is on sale for $39.60. If this price is 55% off the original price, what is the original price of the jacket? 65. Alison needs to make 68 L of a 56% hydrochloric acid solution. How much 8% hydrochloric acid solution and how much 72% hydrochloric acid solution should she mix to get 68 L of a 56% hydrochloric acid solution? 66. Yarrish has a 78% acid solution. He needs 143 L of a 24% acid solution. How many liters of water and how many liters of the 78% acid solution should he mix together to obtain 143 L of a 24% acid solution? 67. The passenger volume at a major international airport was 41.89 million in 2005 and 47.81 million in 2010. What is the percent increase in the passenger volume from 2005 to 2010? Round to one hundredth of a percent. 68. The passenger volume at an airport in Michigan was 36.39 million in 2005 and 35.14 million in 2011. What is the percent decrease in the passenger volume from 2005 to 2011? Round to one hundredth of a percent. 69. A campus bookstore sells an elementary algebra text for $93.60. This is a 30% markup on the cost the bookstore pays for the text. What does the bookstore pay for the text? 70. A campus bookstore sells a chemistry text for $125.35. This is a 15% markup on the cost the bookstore pays for the chemistry text. What does the bookstore pay for the text? 71. Jeanette leaves her job and heads west at 48 mph. Thirty minutes later, Warren leaves the same workplace and heads west at 68 mph. How long will it take Warren to catch up with Jeanette? 72. A plane leaves Newark heading to Las Vegas at 7 a.m. traveling at 320 mph. A second plane leaves Newark heading to Las Vegas at 8:18 a.m. the same day traveling at 580 mph. How long will it take for the second plane to catch up with the first plane? You Be the Teacher! Correct each student’s errors, if any. 73. The price of a 2010 SUV plus 8% sales tax is $52,629.48. Find the price of the car without tax. Emma’s work: sales tax = 52,629.48(8%) = 52,629.48(0.08) = 4210.3584 ≈ 4210.36 Price before tax = 52,629.48 - 4210.36 = 48,419.12 74. A 32-in. LCD-HDTV is on sale for $209.99. This is 40% off the original price. Find the original selling price of the TV. Cynthia’s work: Original selling price = 209.99 40% = 209.99 0.4 = 524.975 ≈ 524.98 75. The passenger volume an international airport in Florida was 30.17 million in 2004 and 34.06 million in 2011. Find the percent increase in the passenger volume from 2004 to 2011. Ralpha’s work: Averge percent = 34.06 - 30.17 34.06 = 3.89 34.06 = 0.114210 ≈ 11.4% 76. Haazim has $13,850 to invest. He invests part of the money in a stock that pays 4.5% annual dividends and the rest of the money in a mutual fund that pays 3.8% annual dividends. If he earns $581.95 in dividends in 1 yr, find the amount invested in each account. Haazim’s work: Let x be the amount invested in the stock and x – 13,850 in the mutual fund account. 4.5x + 3.8(x - 13850) = 581.95 4.5x + 3.8x - 52630 = 581.95 8.3x = 53211.95 x ≈ 6411.08 77. Shan needs to make 210 L of a 60% acid solution. Calculate the number of liters of pure acid and the number of liters of 40% solution Shan needs to mix together to get 210 L of a 60% acid solution. Shan’s work: Let x be the number of liters of pure acid and x - 210 be the number of liters of 40%. 0x + 0.40(x - 210) = 0.60(210) 0.40x - 84 = 126 0.40x = 210 x = 210/0.40 x = 525
hendricks_beginning_algebra_1e_ch1_3
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