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This word equation is called a verbal model .

U SING A P ROBLEM S OLVING P LAN. This word equation is called a verbal model. The verbal model is then used to write a mathematical statement, which is called an algebraic model.

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This word equation is called a verbal model .

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  1. USING A PROBLEM SOLVING PLAN This word equation is called a verbal model. The verbal model is then used to write a mathematical statement, which is called an algebraic model. It is helpful when solving real-life problems to first write an equation in words before you write it in mathematical symbols. WRITE A VERBAL MODEL. ASSIGN LABELS. WRITE AN ALGEBRAIC MODEL. SOLVETHE ALGEBRAIC MODEL. ANSWER THE QUESTION.

  2. Writing and Using a Formula The Bullet Train runs between the Japanese cities of Osaka and Fukuoka, a distance of 550 kilometers. When it makes no stops, it takes 2 hours and 15 minutes to make the trip. What is the average speed of the Bullet Train?

  3. Writing and Using a Formula = • Rate Time Distance LABELS Distance = 550 (kilometers) (kilometers per hour) Rate = r Time = 2.25 (hours) ALGEBRAIC MODEL d r t • = 550 r (2.25) = 550 = r 2.25  r 244 You can use the formulad = rtto write a verbal model. VERBAL MODEL Write algebraic model. Divide each side by 2.25. Use a calculator. The Bullet Train’s average speed is about 244 kilometers per hour.

  4. Writing and Using a Formula 244 kilometers • 550 kilometers  2.25 hours hour You can use unit analysis to check your verbal model. UNIT ANALYSIS

  5. USING OTHER PROBLEM SOLVING STRATEGIES When you are writing a verbal model to represent a real-life problem, remember that you can use otherproblem solving strategies, such as draw a diagram, look for a pattern, or guess, check and revise, to helpcreate a verbal model.

  6. Drawing a Diagram RAILROADSIn 1862, two companies were given the rights to build a railroad from Omaha, Nebraska to Sacramento, California. The Central Pacific Company began from Sacramento in 1863. Twenty-four months later, the Union Pacific company began from Omaha. The Central Pacific Company averaged 8.75 miles of track per month. The Union Pacific Company averaged 20 miles of track per month. The companies met in Promontory, Utah, as the 1590 miles of track were completed. In what year did they meet? How many miles of track did each company build?

  7. Central Pacific Union Pacific Drawing a Diagram Total miles of track = • Number ofmonths Number of months Miles per month Miles per month • LABELS Total miles of track = 1590 (miles) Central Pacific rate = 8.75 (miles per month) Central Pacific time = t (months) Union Pacific rate = 20 (miles per month) Union Pacific time = t – 24 (months) ALGEBRAIC MODEL 1590 = 8.75 t + 20 (t – 24) VERBAL MODEL + Write algebraic model.

  8. Drawing a Diagram 1590 = 8.75 t + 20 (t – 24) ALGEBRAIC MODEL Write algebraic model. 1590 = 8.75 t+ 20 t – 480 Distributive property 2070 = 28.75 t Simplify. 72 =t Divide each side by 28.75. The construction took 72 months (6 years) from the time theCentral Pacific Company began in 1863. They met in 1869.

  9. Drawing a Diagram The number of miles of track built by each company is as follows: 8.75 miles Central Pacific: • 72 months month 20 miles • (72 – 24) months Union Pacific: month The construction took 72 months (6 years) from the time The Central Pacific Company began in 1863. = 630 miles = 960 miles

  10. Looking for a Pattern SOLUTION Look at the differences in the heights given in the table. Story Lobby 1 2 4 3 20 68 Height to top of story (feet) 44 20 32 56 44 56 32 68 32 44 56 After the lobby, the height increases by 12 feet per story. The table gives the heights to the top of the first few stories of a tall building. Determine the height to the top of the 15th story. 12 12 12 12

  11. Looking for a Pattern + • = Height to top of a story Height of lobby Height per story Story number Height to top of a story = h LABELS (feet) Height of lobby = 20 (feet) Height per story = 12 (feet per story) (stories) Story number = n ALGEBRAIC MODEL h 20 12 n = + You can use the observed pattern to write a model for the height. VERBAL MODEL Write algebraic model. Substitute 15 for n. = 20 + 12 (15) = 200 Simplify. The height to the top of the 15th story is 200 feet.

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