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# 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.

Last updated date: 10th Aug 2024
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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.

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 $x.$