112 CHAPTER 1 Equations and Inequalities Work each problem. Round to the nearest tenth of a degree if necessary. 67. Temperature of Venus Venus is the hottest planet, with a surface temperature of 867°F. What is this temperature in degrees Celsius? (Data from The World Almanac and Book of Facts.) 68. Temperature at Soviet Antarctica Station The lowest temperature recorded at the Soviet Antarctica Station of Vostok was -89.2°C. Find the corresponding Fahrenheit temperature. (Data from The World Almanac and Book of Facts.) 69. Temperature in South Carolina A record high temperature of 113°F was recorded for the state of South Carolina on June 29, 2012. What is the corresponding Celsius temperature? (Data from U.S. National Oceanic and Atmospheric Administration.) 70. Temperature in Haiti The average annual temperature in Port-au-Prince, Haiti, is approximately 28.1°C. What is the corresponding Fahrenheit temperature? (Data from www.haiti.climatemps.com) Celsius and Fahrenheit Temperatures In the metric system of weights and measures, temperature is measured in degrees Celsius 1°C2 instead of degrees Fahrenheit 1°F2. To convert between the two systems, we use the equations C = 5 9 1F - 322 and F = 9 5 C + 32. In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. 61. 20°C 62. 200°C 63. 50°F 64. 77°F 65. 100°F 66. 350°F 1.2 Applications and Modeling with Linear Equations ■ Solving Applied Problems ■ Geometry Problems ■ Motion Problems ■ Mixture Problems ■ Modeling with Linear Equations Solving Applied Problems One of the main reasons for learning mathematics is to be able to use it to solve application problems. While there is no one method that enables us to solve all types of applied problems, the following six steps provide a useful guide. Solving an Applied Problem Step 1 Read the problem carefully. What information is given? What is to be found? Step 2 Assign a variable to represent the unknown value, using diagrams or tables as needed. Write down what the variable represents. If necessary, express any other unknown values in terms of the variable. Step 3 Write an equation using the variable expression(s). Step 4 Solve the equation. Step 5 State the answer to the problem. Does it seem reasonable? Step 6 Check the answer in the words of the original problem.
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