## Sunday, 22 February 2009

### Algebra Is Useful

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There are everyday events that requires the use of algebra.

Solving simple math question with unknowns can be done easily with algebra in mind.

Take the example of the math challenge 15 given by clicking this link.

What the challenge requires is the addition of a pair of 2-digit number obtained from a 4-digit number.
The higher 2-digit number is to be added to the lower 2-digit number to obtain the centre 2-digit number.

Example:
1978

Upper 19 is added to lower 78 to produce centre 97.

In that post, you are to come out with more examples of this type of 4-digit numbers.

Use of Algebra can easily solve this cahllenge.

How?

Here it goes...

As in algebra, let's assign "letter" to each digit of this 4-digit number ==> abcd

The upper pair is then 10a + b, and
the lower pair is 10c + d.

Adding them up gives, 10a + b + 10c + d = 10b + c (this is the requirement)
==> 10a + d = 9b - 9c -----(A)

Also a + c + 1 = b ==> a = b - c - 1 -------(B)
and b + d = c + 10 ==> d = c + b + 10 ----(C)

Here, it is necessary to assume b + d >10, since otherwise negative number relation will appear.
(If you find this statement tough, never mind, and read on..)

From the above 3 equations formed, you will then be able to randomly choose numbers that fit them.

You will now appreciate the usefulness of algebra in solving this math challenge.

Enjoy!
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