1. Problem Solving Using Algebraic Models

2. Corporate Average Fuel Economy (CAFE) standards require auto manufacturers to produce cars so that the average fuel efficiency between all of its car models is at least 27.5 miles per gallon. Your new car travels about 385 miles on 11 gallons of gas. Is your car above or below the CAFE standard? Verbal Model Total miles Fuel Efficiency = ÷ # Gallons

3. Verbal Model Total miles Fuel Efficiency = ÷ Labels Fuel efficiency = x Total miles = 385 Amount of gas = 11 (miles/gallon) (miles) (gallons) Alg. Model x = 385 11 x = 35 miles/gallon # Gallons Above CAFE standards.

4. You used all of a $50 gift certificate watching movies at the local theater. You have watched a total of 10 movies. How much did you spent watching evening showings if afternoon showings are $4 and evening showings are $6. Verbal Model $ evening Total $ = ● # evening shows $ afternoon + ● # afternoon shows

5. Verbal Model $ evening Total $ = ● # evening showings $ afternoon + ● # afternoon showings Labels Total cost = 50 Movie cost (evening) = $6 # Movies (evening) = x Movie cost (afternoon) = $4 # Movies (afternoon) = 10 - x

6. Labels Total cost = 50 Movie cost (evening) = $6 # Movies (evening) = x Movie cost (afternoon) = $4 # Movies (afternoon) = 10 - x Alg. Model 50 = 6x + 4(10 – x) 50 = 6x + 40 – 4x 50 = 2x + 40 10 = 2x 5 = x

7. You watched 5 evening showings. The cost was 5(6) = $30.

8. Driving to a concert, you average 24 miles per hour in the city and 65 miles per hour on the highway. If the 142 mile trip takes 2.5 hours, how much of the time were you driving on the highway? Verbal Model Miles/ hr hwy Distance = ● time (hwy) Miles/ hr city + ● time (city)

9. Verbal Model Miles/ hr hwy Distance = ● time (hwy) Miles/ hr city + ● time (city) Labels Distance traveled = 142 Miles/hr (hwy) = 65 Time (hwy) = x Miles/hr (city) = 24 Time (city) = 2.5 - x

10. Labels Distance traveled = 142 Miles/hr (hwy) = 65 Time (hwy) = x Miles/hr (city) = 24 Time (city) = 2.5 - x Alg. Model 142 = 65x + 24(2.5 – x) 142 = 65x + 60 – 24x 142 = 41x + 60 82 = 41x 2 = x

11. You were driving on the highway for 2 hours and driving in the city for 2.5 – 2 = ½ hour.

12. A car and a truck are 245 miles apart traveling towards each other until they meet. The car averages 65 miles per hour and the truck averages 55 miles per hour. The truck started one hour after the car. After how long do the two automobiles meet? How many miles did each automobile travel? Verbal Model rate of car Distance = ● time (car) rate of truck + ● time (truck)

13. Verbal Model rate of car Distance = ● time (car) rate of truck + ● time (truck) Labels Distance traveled = 245 Rate (car) = 65 mph Time (car) = x hr. Rate (truck) = 55 mph Time (truck) = (x – 1) hr.

14. Labels Distance traveled = 245 Rate (car) = 65 mph Time (car) = x hr. rate (truck) = 55 mph Time (truck) = (x – 1) hr. Alg. Model 245 = 65x + 55(x - 1) 245 = 65x + 55x - 55 245 = 120x - 55 300 = 120x 2.5 = x

15. The car traveled for 2.5 hours and the truck traveled for 2.5 – 1 = 1.5 hours before they met. The car traveled 65(2.5) = 162.5 miles. The truck traveled 55(1.5) = 82.5 miles. McDougal Littell/Houghton Mifflin Algebra 2 Notetaking Guide