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 3: x - 46 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.

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

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

47+47+1+45=140
47x3-1=140

Example 2 (confirmation 2):
x=48
48x48x48x48=5308416
48x48x48=110592