The coach of the cricket team buys $ 3 $ bats and $ 6 $ balls for ₹ $ 3900. $ Later, she buys another bat and $ 3 $ more balls of the same kind for ₹ $ 1300. $ Represent this situation algebraically.

Hint: Read the word problem carefully. Denote the cost of bats by one variable and the cost of balls by another variable. Then find a relationship between them. Then solve it to get the solution.

Complete step-by-step answer:
Case 1.
 When the coach of the cricket team buys $ 3 $ bats and $ 6 $ ball for ₹ $ 3900. $
Let the cost of bat $ = x $ ₹
And the cost of ball $ = y $ ₹
Then, we write an equation form given the condition.
 $ 3x + 6y = 3900 $ . . . (1)
Case 2.
When she buys another bat and $ 3 $ same ball of some kind for ₹ $ 1300 $ .
Now, with the help of above condition we get,
 $ \Rightarrow x + 3y = 1300 $ . . . (2)
By rearranging the equation,
 $ x = 1300 - 3y $ .
Then put the value of $ x $ in equation (1).
 $ \Rightarrow 3(1300 - 3y) + 6y = 3900 $
 $ 3900 - 9y + 6y = 3900 $
On simplifying above equation we get,
 $ y = 0 $
Put the value of $ y $ in (2) we get,
 $ x = 1300 $
Hence, if the cost of bats is ₹1300 and cost of ball is zero₹.

Note: It is important to interpret the question properly. A small mistake can lead to incorrect answers. The linear equation in this question can also be solved by multiplying equation (2) by $ 3 $ and then subtracting it from (1) to get the value of $ y $ . Then we could put that $ y $ into equation (2) to get $ x. $