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Solving Real-World Problems with Systems of Equations

This guide provides a step-by-step approach to translating and solving problems using systems of equations. We will explore practical examples including the relationship between the number of mini-buses and regular buses at Yellow Bus Company, the sales figures of an automobile dealer, and age-related problems between friends and siblings. By breaking down complex scenarios into manageable equations, you will learn how to find solutions to real-world problems. Practice problems are included to test your understanding and skills.

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Solving Real-World Problems with Systems of Equations

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  1. Using Systems of Equations Objectives: To solve problems using systems of equations

  2. Example 1 Translate into a system of equations and solve. The Yellow Bus company owns three times as many mini-buses as regular buses. There are 60 more mini-buses than regular buses. How many of each does Yellow Bus own? Let m be the number of mini-buses Let r be the number of regular buses m = 3r m = r + 60 m = 3r 3r = r + 60 m = 3(30) 2r = 60 m =90 r = 30 30 regular buses, 90 mini-buses

  3. Practice Translate into a system of equations and solve. An automobile dealer sold 180 vans and trucks at a sale. He sold 40 more vans than trucks. How many of each did he sell?

  4. Example 2 Translate into a system of equations and solve. Bob is 6 years older than Fred. Fred is half as old as Bob. How old are they? Let b be the age of Bob Let f be the age of Fred b = f + 6 b = f + 6 b = 2f b = (6) + 6 f + 6 = 2f 6 = f b = 12 Bob is 12. Fred is 6.

  5. Example 3 Translate into a system of equations and solve. Fran is two years older than her brother. Twelve years ago she was twice as old as he was. How old are they now? f f - 12 b - 12 b f = b + 2 b = 14 f – 12 = 2(b – 12) f = b + 2 f = 14 + 2 (b + 2) – 12 = 2(b – 12) f = 16 b – 10 = 2b – 24 b = 2b – 14 Fran is 16; brother is 14

  6. Practice Translate into a system of equations and solve. Wilma is 13 years older than Bev. In nine years, Wilma will be twice as old as Bev. How old is Bev?

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