Wednesday, 17 February 2016

Algebra... Different "Faces" of Algebra (I)

The total length of 4 roads is (3x - 1) km.
What are the possible lengths of the 4 roads in kilometres?
Note that x is an integer.

e.g. The length of the 4 roads are: x km, x km, x-7 km, 6 km
Check: x + x + (x - 7) + 6 = 3x - 1

Enter your suggested lengths in comments.
You may also enter any assumptions you made to your answers.

39 comments:

  1. The length of the 4 roads are:
    x-5 km, x km, x km, 4 km
    Check: x + x + x-5 + 4 = 3x-1

    ReplyDelete
    Replies
    1. You are correct.
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
  2. The possible lengths of the 4 roads are:
    Xcm
    (X-10)cm
    (X+5)cm
    4cm
    Check:(X+(X-10)+(X+5)+4)cm =3x-1

    ReplyDelete
    Replies
    1. You are correct.
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
    2. The assumptions I made were
      X is a positive integer
      X is larger than 10

      Delete
  3. The possible lengths are:
    Xkm
    (X-8)km
    7km
    Xkm
    check:
    X+X+X+7-8=(3X-1)km

    ReplyDelete
    Replies
    1. You are correct.
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
  4. Possible lengths:
    x km
    x km
    (x-2) km
    1 km
    Check: x+x+x-2+1=(3x-1) km

    ReplyDelete
  5. This comment has been removed by the author.

    ReplyDelete
    Replies
    1. Check:
      Are the proposed measurements valid?
      What's the assumption?

      Delete
  6. x-3,x-8,x and 10km
    Check:3x-(-11)+10=3x(-1)km

    ReplyDelete
    Replies
    1. You are correct.
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
  7. The lengths can be
    1)x
    2)x-4
    3)x-6
    4)9
    Check: (x+(x-4)+(x-6)+9=3x(-1)

    ReplyDelete
  8. The lengths of the roads may be (in km)
    1)x-1
    2)x-2
    3)x-3
    4)5

    ReplyDelete
    Replies
    1. You are correct.
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
  9. The possible lengths of the 4 roads are:
    1) (x-9) km
    2) (x+4) km
    3) (x+2) km
    4) 2km
    Check: ((x-9)+(x+4)+(x+2)+2)km= (3x-1)km

    ReplyDelete
    Replies
    1. You are correct.
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
  10. Replies
    1. Correct.
      What condition(s) do you need to include for the answer?

      Delete
    2. I assume that x is a positive integer and is greater than 7.

      Delete
  11. Possible length of roads:
    1) (X-2)km
    2) (X-2)km
    3) (X-1)km
    4) 4km

    Check: (3X-5+4)km = (3X-1)km

    ReplyDelete
    Replies
    1. However, you can be specific, what assumption(s) did you make about the value of x?

      Delete
  12. Possible lengths: x km, (1x-10)km, 9km, x km
    Check: 9 + x + x +(x-10)= (3x -1)km

    ReplyDelete
    Replies
    1. Check:
      Are the proposed measurements valid?
      What's the assumption?

      Delete
    2. Assuming x is a positive integer and it is greater than 7

      Delete
  13. Possible lengths: x km, (1x-10)km, 9km, x km
    Check: 9 + x + x +(x-10)= (3x -1)km

    ReplyDelete
    Replies
    1. You are correct;
      However, you can be specific, what assumption(s) did you make about the value of x?

      Delete

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