Presentation on theme: "3.6 Equations and Problem Solving"— Presentation transcript:
1 3.6 Equations and Problem Solving Date: ______________
2 Steps to Solve Word Problems Identify the unknownsUse variablesDraw a diagram that will help you understand the problemDetermine the formulas, equations that the problem is dealing withMight be more than oneRead a sentence at a time and make an equation
3 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 = lengthPerimeter Formula:P = 2w + 2lLetw = width26 = 2(l – 3) + 2lw = l - 326 = 2l – 6 + 2lP = 2626 = 4l – 6w = 8 - 332 = 4lw = 5 in8 = l
4 ExamplesThe sum of three consecutive integers is 72. Find the integersConsecutive – in a row, back to backLet n = 1st numbern + n n + 2 = 72n + 1 = 2nd number3n + 3 = 72n + 2 = 3rd number3n = 69n = 2323, 24, 25
5 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 travelsJetRateTimeDistance Traveled1st2ndt – 1 = time the 2nd jet travels180t180t180t = 330(t – 1)330t – 1330(t – 1)180t = 330t – 330- 330t t-150t = -330t = 2.2
6 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?HillRateTimeDistanceUpDownLet t = time you go up the hillLet 3 – t = time you go down the hill4t4t63 – t6(3 – t)4t = 6(3 – t)10t = 184t = 18 – 6t+ 6t tt = 1.8 h10t = 18
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