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Draw a Diagram and Write an Equation

This lesson teaches how to find the length of a trailer when given the total length of the car and trailer, and the car is 9 ft longer than the trailer.

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Draw a Diagram and Write an Equation

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  1. The combined length of the car and trailer is 25 ft. The car is 9 ft longer than the trailer. The goal is to find the length of the trailer. COURSE 3 LESSON 2-5 Draw a Diagram and Write an Equation The length of a car with a small trailer attached is 25 ft. The car is 9 ft longer than the trailer. How long is the trailer? 2-5

  2. COURSE 3 LESSON 2-5 Draw a Diagram and Write an Equation (continued) Method 1 Draw a Diagram Draw a diagram to show that the car with the trailer attached is 25 ft and the car is 9 ft longer than the trailer. 2-5

  3. Method 2 Write an Equation You know that the car is 9 ft longer than the trailer. You also know that the car and trailer are 25 ft long. COURSE 3 LESSON 2-5 Draw a Diagram and Write an Equation (continued) Subtracting 9 ft from 25 ft results in 16 ft, which is twice the length of the trailer. One half of 16 is 8, so the trailer is 8 ft long. 2-5

  4. Words car length plus trailer length is total length Equationt + 9 + t = 25 Let t = the length of the trailer. The car is 9 ft longer than the trailer. 2t+ 9 = 25 Combine like terms. Let t + 9 = the length of the car. 2t + 9 – 9 = 25 – 9Subtract 9 from each side. COURSE 3 LESSON 2-5 Draw a Diagram and Write an Equation (continued) (t + 9) + t = 25 2-5

  5. 2t = 16 Simplify. = 2t 2 16 2 Divide each side by 2. t = 8 Simplify. If the trailer is 8 ft long, then the car is 8 + 9, or 17 ft long. Since 8 + 17 = 25, the answer checks. COURSE 3 LESSON 2-5 Draw a Diagram and Write an Equation (continued) The trailer is 8 ft long. 2-5

  6. COURSE 3 LESSON 2-5 Draw a Diagram and Write an Equation Name two strategies you could use to solve the problem. Then solve the problem. One side of a triangular garden measures 22 ft. A second side is 6 times the third side. The perimeter is 50 ft. What is the length of the shortest side? Strategies may vary. Sample: Draw a diagram and write an equation. 4 ft 2-5

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