## Algebra

Algebra is a very important topic in mathematics. This topic is generally used for solving equations.

Founders :

 The major development of this topic was done in the ninth century by Arab mathematicians. In particular Al-Khwarzmi's book entitled "compendium on a  calculation by completing and balancing" was and significant event in the history of mathematics.So he is considered as the father of algebra.In the sixth and seventh centuries,Indian mathematicians Aryabhatta and Brahmagupta have worked on the topics linear equations and quadratic equations and general method of solving. In the 19th century British mathematicians took great effort on developing this topic. The Peacock was the founder of axiomatic thinking in arithmetic. He is called as Euclid of algebra.

Why we have to study algebra:

To answer this question,let us consider the following practical example

Example:

15 kg of wheat 9 kg of sugar together cost \$ 525. 20 kg of wheat and 10 kg of sugar cost \$ 125 more. Find the costs of wheat and sugar.

To find the cost of wheat and sugar per kg we have to create two linear equations by using the math topic algebra and we have to solve them.

Let us see the procedure

Cost of first purchase = \$ 525

Cost of second purchase = \$ 525 + \$ 125

= \$ 650

Cost of 15 kg wheat + cost of 9 kg sugar = \$ 525

15 x Cost of wheat per kg + 9 x cost of sugar per kg = 525

Cost of 20 kg wheat + cost of 10 kg sugar = \$ 650

20 x Cost of wheat per kg + 10 x cost of sugar per kg = 650

Cost of wheat per kg = \$ x

Cost of sugar per kg = \$ y

15 x + 9 y = 525  --- (1)

20 x + 10 y = 650 --- (2)

Dividing the first equation by 3

5 x + 3 y = 175

Dividing the second equation by 10

2 x + y = 65

5 x + 3 y = 175 --- (1)

(2) x 3=>   6 x + 3 y = 195 ----(3)

(-)     (-)        (-)

----------------------

- x = -20

x = 20

Now we are going to apply the value of x in the first equation

5 x + 3 y = 175

5 (20) + 3 y = 175

100 + 3y = 175

3 y = 175 – 100

3 y = 75

y = 75/3

y = 25

Therefore cost of wheat per kg \$ 20

Cost of sugar per kg  = \$ 25

To solve these kind of problems in real life we have to know about this topic.You can see lots of topics below