���������������������� Solving Applications of Adding Signed Numbers Step 1: Express the problem mathematically. Step 2: Apply the rules for adding signed numbers. �� ������������������������ ������������������ Write a mathematical equation that models the given situation and then find the result. The operating income for Delta Airlines for the years 2002 to 2009 is shown in the table. A negative number represents a loss in operating income. (Source: http://www.airlinefinancials.com/ uploads/2002–2009_Delta_mainline.pdf ) 3a. Find the total operating income (TOI) for the years 2002–2005. 3b. Find the average operating income (AOI) for the years 2007–2009. Solutions 3a. We add the values for the 4 yr. Since the numbers all have the same sign, we add their absolute values and keep the sign. TOI = (-1309) + (-786) + (-5985) + (-1605) TOI=-9685 So, Delta Airlines had a total loss of $9685 million during the years 2002 to 2005. 3b. We add the values for the given years and divide by the number of years, 3. AOI = 78 + (-58) + 605 3 AOI = 625 3 AOI = 208.33 So, Delta Airlines had an average operating income of $208.33 million during the years 2007 to 2009. Student Check 3 Write a mathematical equation that models the given situation and then find the result. The table shows the average monthly low temperature for one of the northernmost points in the United States: Barrow, Alaska. Find the average yearly low temperature. Troubleshooting Common Errors Some common errors associated with adding real numbers are shown next. Objective 4 ▶ Troubleshoot common errors. Year Operating Income (in millions) 2002 –$1309 2003 –$ 786 2004 –$5985 2005 –$1605 2006 –$1139 2007 $ 78 2008 –$ 58 2009 $ 605 Month °F Month °F Jan. -20 July 34 Feb. -22 Aug. 34 Mar. -22 Sept. 28 Apr. -7 Oct. 10 May 15 Nov. -6 June 30 Dec. -16 46 Chapter 1 Real Numbers and Algebraic Expressions
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