1.5 Problem Solving Using Algebraic s Goals Use a general roblem solving lan. Use other roblem solving strategies. Your Notes VOCABULARY model A word equation reresenting a real-life roblem Algebraic model A mathematical statement that reresents a real-life roblem Examle 1 Writing and Using a Simle Cororate Average Fuel Economy (CAFE) standards require auto manufacturers to roduce cars so that the average fuel efficiency between all of its car models is at least 27.5 miles er gallon. Your new car travels about 385 miles on 11 gallons of gas. Is your car above or below the CAFE standard? Algebraic Fuel Total miles efficiency Fuel efficiency x Total miles 385 Amount of gasoline 11 x 385 11 x 35 (miles er gallon) (miles) Amount of gasoline (gallons) Your car s fuel efficiency is 35 miles er gallon, which is above the CAFE standard. Lesson 1.5 Algebra 2 Notetaking Guide 13
Examle 2 Writing and Using a You used all of a $50 gift certificate watching movies at the local theater and you want to know how much you have sent watching evening showings. Afternoon showings are $4 and evening showings are $6. You have seen a total of 10 movies. Total cost Evening showings Number of Movie cost movies Afternoon showings Movie cost Number of movies Total cost 50 Movie cost (evening) 6 Number of movies (evening) x Movie cost (afternoon) 4 Number of movies (afternoon) 10 x Algebraic 50 6x 4(10 x) 50 2x 40 10 2x 5 x You watched 5 evening showings. The cost was 5 (6) $ 30. (movies) (movies) Checkoint Comlete the following exercise. 1. Driving to a concert, you average 24 miles er hour in the city and 65 miles er hour on the highway. If the 142 mile tri takes 2.5 hours, how much of the time were you driving on the highway? 2 hours 14 Algebra 2 Notetaking Guide Chater 1
Examle 3 Drawing a Diagram A car and a truck are 245 miles aart traveling towards each other until they meet. The car averages 65 miles er hour and the truck averages 55 miles er hour. The truck started one hour after the car. After how long do the two automobiles meet? How many miles will each automobile have traveled? Begin by drawing and labeling a diagram. 245 miles Car Meeting oint Car Truck Total distance Miles er Number hour of hours Truck Miles er hour Number of hours Total distance 245 Car rate 65 Car time t Truck rate 55 Truck time t 1 (miles) (miles er hour) (hours) (miles er hour) (hours) Algebraic 245 65t 55(t 1) 245 120t 55 300 120t 2.5 t The automobiles meet after 2.5 hours. The number of miles each will have traveled is as shown. Car: 65 miles 2.5 hours 162.5 miles hour Truck: 55 miles ( 2.5 1 ) hours 82.5 miles hour Lesson 1.5 Algebra 2 Notetaking Guide 15
Checkoint Comlete the following exercise. 2. Assume the truck in Examle 3 left 30 minutes after the car. After how long do the two automobiles meet? about 2.27 hours, or 2 hours 16 minutes Examle 4 Looking for a Pattern The table gives the heights to the to of the first few layers of bricks in a brick wall. Determine the height of 18 layers. Layers Foundation 1 2 3 4 Height to to of layer (inches) 6 9 12 15 18 Look at the differences in the heights given in the table. The height increases by 3 inches er layer. Heights: 6 9 12 15 18 3 3 3 3 Use the observed attern to write a model for the height. Height to to of a layer Height of Height foundation er layer Layer number Height to to of a layer h (inches) Height of foundation 6 (inches) Height er layer 3 (inches er layer) Layer number n (layers) Algebraic h 6 3n Write algebraic model. h 6 3(18) Substitute for n. h 60 Simlify. The height to the to of 18 layers is 60 inches, or 5 feet. 16 Algebra 2 Notetaking Guide Chater 1
Checkoint Comlete the following exercise. 3. The table gives the heights to the to of the first few layers of bricks in a brick wall. Determine the height of 20 layers. Layers Foundation 1 2 3 4 Height to to of layer (inches) 2 7 12 17 22 8 feet 6 inches Homework Lesson 1.5 Algebra 2 Notetaking Guide 17