1.5 problem solving using algebraic models
- 1. Today’s objective: 1. I will use a gener al pr oblem solving plan to solve r eal-life pr oblems.
- 2. When solving real-life problems, it is sometimes helpful to first write an equation in words before you write it in mathematical symbols. Verbal model: a word equation that represents a real-life problem. Algebraic model: a mathematical statement that
- 3. 1. Write a verbal model. 2. Assign labels. 3. Write an algebraic model. 4. Solve the algebraic model.
- 4. The Bullet Train runs Verbal Model between Osaka and Distance = Rate x Time Fukuoka, a distance Labels of 550 kilometers. Distance = 550km When it makes no Rate = r stops, it takes 2 Time = 2.25 hours hours and 15 Algebraic Model minutes to make the 550 = r(2.25) trip. What is the Solve algebraic model average speed of the r = 550/2.25 ≈ 244 Bullet Train? Answer the question The Bullet Train’s average speed is about 244 km/h.
- 5. A water-saving faucet Verbal Model has a flow rate of at Volume = Flow rate x Time most 9.6 cubic inches Labels per second. To test Volume = 470 whether your faucet Rate = r meets this standard, Time = 35 seconds you time how long it Algebraic Model takes the faucet to fill a 470 cubic inch pot, 470 = r(35) obtaining a time of 35 Solve algebraic model seconds. Find your r = 470/35 ≈ 13.4 faucet’s flow rate. Answer the question Does it meet the The flow rate is about 13.4 standard for water in.3/s, which does not meet conservation? the standard.