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Let us suppose that the amount of the first prize be INR x. Since each prize value after the first prize is INR 200 less than the preceding prize. Thus, the amounts of the four prizes are in arithmetic progression means AP.

Thus according to the question,

Amount of the second prize will be x- 200.

Amount of the third prize will be x - 200 - 200 = x - 400.

Amount of the fourth prize will be x- 400 – 200 = x-600.

Now, as given in the question that the total sum of prizes is INR 2800.

So by the condition given in the question, we have

\[

x + \left( {x - 200} \right) + \left( {x - 400} \right) + \left( {x - 600} \right) = 2800 \\

\Rightarrow 4x - 1200 = 2800 \\

\Rightarrow 4x = 4000 \\

\Rightarrow x = 1000 \\

\]

Hence, we got the value of an unknown variable of the above equation, x as 1000.

Amount of the first prize will be, x = INR 1000

Amount of the second prize will be, x- 200 = 1000-200 = INR 800.

Amount of the third prize will be, x – 400 = 1000-400= INR 600.

Amount of the fourth prize will be, x- 600 = 1000-600= INR 400.

* Linear equations in one variable are in the form $ax+b=0$.

* Linear equations in two variables are in the form $ax+by+c=0$.