slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Problem Solving Using Algebraic Models PowerPoint Presentation
Download Presentation
Problem Solving Using Algebraic Models

Loading in 2 Seconds...

play fullscreen
1 / 15

Problem Solving Using Algebraic Models - PowerPoint PPT Presentation


  • 116 Views
  • Uploaded on

Problem Solving Using Algebraic Models.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Problem Solving Using Algebraic Models' - armina


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Problem Solving Using

Algebraic Models

slide2

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

slide3

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.

slide4

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

slide5

# 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

slide6

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

slide7

You watched 5 evening showings.

The cost was 5(6) = $30.

slide8

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)

slide9

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

slide10

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

slide12

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)

slide13

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

slide14

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

slide15

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