3.6 Equations and Problem Solving Date: ______________

Steps to Solve Word Problems Identify the unknowns Use variables Draw a diagram that will help you understand the problem Determine the formulas, equations that the problem is dealing with Might be more than one Read a sentence at a time and make an equation

Examples Perimeter Formula: P = 2w + 2l w = l - 3 26 = 2l – 6 + 2l The width of a rectangle is 3 in. less than its length. The perimeter of the rectangle is 26 in. What is the width of the rectangle. Let l = length Perimeter Formula: P = 2w + 2l Let w = width 26 = 2(l – 3) + 2l w = l - 3 26 = 2l – 6 + 2l P = 26 26 = 4l – 6 w = 8 - 3 32 = 4l w = 5 in 8 = l

Examples The sum of three consecutive integers is 72. Find the integers Consecutive – in a row, back to back Let n = 1st number n + n + 1 + n + 2 = 72 n + 1 = 2nd number 3n + 3 = 72 n + 2 = 3rd number - 3 - 3 3n = 69 3 3 n = 23 23, 24, 25

Examples 180t = 330(t – 1) 180t = 330t – 330 - 330t - 330t An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left 1 hour later. The jet follows the same route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane? Let t = time the 1st plane travels Jet Rate Time Distance Traveled 1st 2nd t – 1 = time the 2nd jet travels 180 t 180t 180t = 330(t – 1) 330 t – 1 330(t – 1) 180t = 330t – 330 - 330t - 330t -150t = -330 t = 2.2

Examples 4t = 6(3 – t) 10t = 18 4t = 18 – 6t 10 10 + 6t + 6t t = 1.8 h Suppose you hike up a hill at 4 km/h. You hike back down at 6 km/h. Your hiking trip took 3 hours. How much time did it take you to hike up the hill? Hill Rate Time Distance Up Down Let t = time you go up the hill Let 3 – t = time you go down the hill 4 t 4t 6 3 – t 6(3 – t) 4t = 6(3 – t) 10t = 18 4t = 18 – 6t 10 10 + 6t + 6t t = 1.8 h 10t = 18