The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.

9514 1404 393Answer:(x -3) +(x -1) +(x +1) +(x +3) = -72-21, -19, -17, -15Step-by-step explanation:Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is ...   (x -3) +(x -1) +(x +1) +(x +3) = -72   4x = -72   x = -18The four integers are -21, -19, -17, -15._____Additional commentYou could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a "subtract 12" step in the solution process that is unnecessary if x is chosen to be the average of the integers. As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.