## Monday, 25 March 2013

### Algebra: Is the Problem Obvious?

Do you think Mr Kanbili is fair and Mr Ong should accept the suggestion?
2. Give an example to illustrate your stand.
3. Explain how you come to this conclusion (Hint: Use algebra).

1. Mr kanbili is not fair to Mr Ong.

what he promised is eg :
a x a = a^2

what he actually offered is eg :
[a-1] x [a+1] = a^2 + a -a - 1
= a^2 - 1

the real one is 1m^2 smaller than what Mr Kanbili offered therefore he is not being fair

2. This comment has been removed by the author.

3. a^2 = a^2

(a-2) x (a+2) = a(a+2) - 2(a+2)
= (a^2 + 2a) - (2a + 4)
= a^2 + 4

a^2 is not = to (a^2+4)

== MR KANBII!!!

1. *a^2 = a^2

(a-2) x (a+2) = a(a+2) - 2(a+2)
= (a^2 + 2a) - (2a - 4)
= a^2 - 4

a^2 is not = to (a^2 - 4)

== MR KANBII!!!

4. let the length be A
If the field is rectangle the total area is a^2+1 while the square is a^2

5. 1.I think that he should not accept the deal.
2.After calculations, I found out that it was 25m^2.
3.I am not sure.

1. Sorry, I mean that if it was 5m short.

6. Its not fair because:

Initial offer = x^2

However, his last offer was (x-1)*(x+1)
So lets say that x was 40 as stated in the video^
Thus in conclusion it is 39x41, and it is smaller than 40^2

So its unfair towards Mr Ong

7. Mr Kanbili is not being fair.
At first, it was axa=a^2
However, what was given was: (a-1)x(a+1)=a^2-1
The 2nd one was 1m^2 , so that is not fair ._.

8. I don't think Mr Kanbili is not fair.

He promised Mr Ong a square, which is eg. a*a

But what Mr Kanbili gave was a rectangle which is (a+1)*(a-1)

9. Mr kanbili is not fair to Mr Ong.
What Mr Kanbili promised:
axa=a^2
What he actually offered:
(a-1)x(a+1)=a^2+a-a-1
=a^2-1

the land offered is 1m^2 smaller so he is not fair.

10. 1. What is your stand?
Mr Ong should not accept the suggestion.

2. Give an example to illustrate your stand.
For the square:
Take 40m to be x. If you buy the square, it would be x^2.
For the rectangle:
One side to be 40m - 4m = 36m. It is represented by x - 4. The other side would be 40m + 4m = 44m. It is represented by x + 4. The whole area of it would be x^2 - 16.
This proves that the square is bigger no matter what, and buying the rectangle is not worth it.

3. Explain how you come to this conclusion (Hint: Use algebra).
I used algebra to compare.

11. 1. What is your stand?
Mr. Ong should not accept the suggestion.

2. Give an example to illustrate your stand.
Let the length of one side of the field to be "a"
Let the length reduced / increased be "b"
The original area of the field promised was - a*a= a^2

so, for the rectangle the area would be -
(a+b)(a-b) = a(a-b) + b(a-b)
= a^2 -ab +ab -b^2
= a^2 - b^2

The area is lower than the promised value!
SO, MR Kanbili IS A CHEATER!!!!

12. 1. Mr Kambili is conning Mr Ong
2. 2X3 is not equal to 1X4
3.The actual area is (40-x)X(40+X)=1600-X^2 and the stated total area is 1600. Henceforth, Mr Ong is being conned

13. 1. Mr Kambili is not being fair to Mr Ong.
2. Assume the length of the square is x, the area as promised by Mr Kambili will be x^2. But if i is a rectangle and assume that the few metres that are less are 2m. So if the area is a rectangle, (x-1)(x+1) is (x^2-1). So Mr Kambili is not being fair.
3. I used algebra.

14. I think Mr Ong should not accept the offer.

Take x to be 40m, y to be 50m and z to be 30m.

The square field will be x^2 while the rectangular field will be yz

The area: square field: 1600m^2 while rectangular field will be 1500m^2

15. 1. Mr Kanbili is cheating Mr Ong.
2. Let say the length is 1m shorter going north but 1m longer going east, which means 39x41. 39x41=1599 , which is shorter than 40x40, which is equal to 1600.
3. Let the length be L. L^2 is not equal to (L-1)(L+1), SO Mr Kanbili is cheating Mr Ong.

16. Mr Kanbili is not being fair.

Initially, it was axa=a^2
However, what was given was- (a-1)x(a+1)=a^2-1
The 2nd one was 1m^2.
In conclusion, it is not a fair offer.

17. Mr Kanbili is not being fair to Mr Ong

Let x be 40m
x*x= x^2
(x-1)(x+1)=x^2-1

The real one offered is 1m^2 shorter than what Mr Kanbili offered
So in conclusion don't trust Mr kanbili. He would definitely CHEAT Mr Ong.

18. Mr Kanbilli cheated Mr Ong.
The area of the land is supposed to be a^2.
However it is ; (a-1)(a+1)
=a^2+a-a-1
=a^2-1
Therefore, Mr Kanbilli gave Mr Ong a field of lesser area.

19. Mr Ong was cheated.
Let the length of the field be a
and the number mr kanbilli increased/decreased be b.
a*a=a^2
(a-b)(a+b)=a^2-b^2
SO Mr Kanbilli cheated Mr ong!