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:
*x*⁴÷*x*³ 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.

I think the value is 133333333

ReplyDeleteSince 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

Part 1:

ReplyDeletex 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.