Verbal Models Linear Equations

1
Verbal Models Linear Equations

• Section 3.5

2

• A page of your school yearbook is 8 1/2 inches by
  11 inches. The left margin is ¾ inch and the
  space to the right of the pictures is 2 7/8. The
  space between pictures is 3/16 inch. How wide
  can each picture be to fit three across the width
  of the page?
• Strategy Draw a picture

3
Yearbook Picture
3/16
3/16
3/4
2 7/8
w
w
w
4
Verbal Model

• Left Margin Space to right 2 Space between
  3 picture Page
• of pictures pictures width
  width
• Labels ¾ 2 7/8 2
  ( 3/16) 3 (w) 8 ½
• ¾ 2 7/8 2 x 3 3w 8 1/2
• 1 16
• ¾ 2 7/8 3/8 3w 8 1/2
• 6/8 2 7/8 3/8 3w 8 ½
• 16/8 2 3w 8 ½
• 2 2 3w 8 ½
• 4 3w 8 ½
• -4 -4
• 3w 4 ½
• 3w 9/2
• 1/3 (3w) 9/2(1/3)
• W 3/2
• W 1 1/2

5
Gazelle and Cheetah

• A gazelle can run 73 feet per second for several
  minutes. A cheetah can run faster (88 feet per
  second) but can only sustain its top speed for
  about 20 seconds before it is worn out. How far
  away from the cheetah does the gazelle need to
  stay for it to be safe?
• Draw a picture

6
Draw a picture
x
If the gazelle is closer to the Cheetah than x
feet, the cheetah can reach the gazelle.
If the gazelle is farther away than x feet, the
gazelle is in the safety zone.
Gazelle caught in 20 seconds
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D RT

• To find the safety zone you have to find the
  cheetahs distance run in 20 seconds.
• D RT
• X 88 (20)
• X 1760
• The Gazellas distance in 20 seconds
• D RT
• X 73 (20)
• X 1460
• Remember these for next slide!!!

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Verbal Model

• Distance gazelle Gazelles starting
  Distance Cheetah
• runs in 20 sec distance from Cheetah runs in
  20 sec.
• LABELS
• 1460 N
  1760
• 1460 - 1460
• N 300
• The gazelle needs to stay more than 300 feet
  away.

9
Rabbit and Coyote

• A rabbit is 30 feet from its burrow. It can run
  25 feet per second. A coyote that can run 50 feet
  per second spots the rabbit and starts running
  toward it.

30 ft
x feet
10

• Write an expression for the time it will take the
  rabbit to get to its burrow.
• D rt
• 30 25 t
• 1.2t
• Write an expression for the time it will take the
  coyote to get to the burrow.
• D r t
• X 30 50 t
• X30 t
• 50

11

• If the two times are equal the rabbit will get to
  the hole as the coyote does.
• 1.2 x 30
• 50
• 1.2 (50) x 30 (50)
• 50
• 60 x 30
• -30 -30
• 30 x
• Therefore, the distance between the rabbit and
  the coyote must be more than 30 feet in order for
  the rabbit to make it to his hole safely.