Chap 5 Algebra: 6 A.M. QUIZ (23 May 2010) (IV)

In the activity Chap 5 Algebra... Different "Faces" of Algebra (II),
The total length of 4 roads is (3x - 1) km. What are the possible lengths of the 4 roads in kilometres?

The lengths of the 4 roads that Joshua Loh gave were:

  • Road 1: x⁴÷ x³ km
  • Road 2: x km
  • Road 3: x - 46 km
  • Road 4: 45 km

However, his answer is only true for some values of x.

  • What values of x must his answers take so that the answers are true?
  • Then why not other values of x?

Note: This is a 3-mark question.

2 comments:

  1. I think the value is 133333333
    Since 3x-1 = x4 ÷ x3 + x + x -46 +45
    x -46 + 45 = x -1
    X-1 +X = 2x -1
    X4 ÷ x3 = 1.33333333
    1.33333333 x 100000000 = 133333333
    I think it is not the other values as 1 is not plausible as x4 ÷ x3 is not 1 but 1.33333333. The other values also do not get the same value as x 4 ÷x3

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  2. Part 1:
    x can be any number more than 46.
    Example (confirmation 1):
    x=47
    47x47x47x47=4879681
    47x47x47=103823
    4879681÷103823=47 (road 1,road 2)

    47-46=1 (road 3)
    45 (road 4)
    47+47+1+45=140
    47x3-1=140

    Example 2 (confirmation 2):
    x=48
    48x48x48x48=5308416
    48x48x48=110592
    5308416÷110592=48 (road 1,road 2)

    48-46=2 (road 3)
    45 (road 4)
    48+48+2+45=143
    48x3-1=143

    Part 2:
    The value of x cannot be anything 46 and below as the equation for road 3 would be wrong. Example, x is 46. the equation for road 3 would be 46-46, which is 0. It would be impossible for a road to be 0km. If you apply the same method to 45 or below, the answers for the length of road 3 would be negative answers. Therefore I conclude that the values for x can be any number as long as it is above 46.

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