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On Monday, Avi walked from his home to the school track and walked
4 laps around the track for a total of 3.5 miles. On Saturday, Avi ran from
his home to the school track, ran 2 laps, and then ran home for a total of
4 miles. Let x represent the distance from Avi’s home to the school track,
and let y represent the distance of one lap around the track.

1. Write a system of equations to represent this situation.

2. What is the distance from Avi’s home to the school track and around
the track?

3. On Saturday, Avi walked from his home to the school track, walked 6
times around the track, and then walked home. How far did he walk in all?

Avi knows that the distance from his home to the library and back is
at least 2.5 miles. He also knows that the distance from his home to
the library and then to the school track is less than 3 miles. Let p
represent the distance from Avi’s home to the library, and let q
represent the distance from the library to the school track.

4. Write a system of inequalities to represent this situation.

5. Can the distance from Avi’s home to the library be 2 miles and the
distance from the library to the school track be 1 mile?

Respuesta :

sqdancefan

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Answer:

  1. x+4y=3.5; 2x+2y=4
  2. x=1.5; y=0.5
  3. 6 miles
  4. 2p≥2.5; p+q<3
  5. No

Step-by-step explanation:

1. x +4y = 3.5 . . . . variables are defined in the problem statement

  2x +2y = 4

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2. Subtract half the second equation from the first.

  (x +4y) -(1/2)(2x +2y) = (3.5) -(1/2)(4)

  3y = 1.5

  y = 0.5

  x = 2 -y = 1.5

The distance from home is 1.5 miles; the distance around the track is 0.5 miles.

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3. 2x +6y = 2(1.5) +6(0.5) = 3+3 = 6

Avi walked 6 miles on Saturday.

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4. 2p ≥ 2.5 . . . . variables are defined in the problem statement

  p +q < 3

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5. No.

  2 + 1 < 3 is NOT TRUE

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