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Problem Solving Using Algebraic Models

Problem Solving Using Algebraic Models.

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Problem Solving Using Algebraic Models

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  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 Fuel Efficiency Total miles ÷ = # Gallons

  3. Verbal Model Fuel Efficiency Total miles ÷ = # Gallons Fuel efficiency = x Total miles = 385 Amount of gas = 11 Labels (miles/gallon) (miles) (gallons) Alg. Model x = 385 11 x = 35 miles/gallon 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. # evening shows = Verbal Model Total $ $ evening ● # afternoon shows + $ afternoon ●

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

  6. Total cost = 50 Movie cost (evening) = $6 # Movies (evening) = x Movie cost (afternoon) = $4 # Movies (afternoon) = 10 - x Labels 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? Miles/hr hwy = Verbal Model Distance time (hwy) ● Miles/hr city + time (city) ●

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

  10. Distance traveled = 142 Miles/hr (hwy) = 65 Time (hwy) = x Miles/hr (city) = 24 Time (city) = 2.5 - x Labels 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? rate of car = Verbal Model Distance time (car) ● rate of truck + time (truck) ●

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

  14. Distance traveled = 245 Rate (car) = 65 mph Time (car) = x hr. rate (truck) = 55 mph Time (truck) = (x – 1) hr. Labels 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

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