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The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, he buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.

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Hint: Assume a variable x which represents the cost of each bat and assume a variable y which represents the cost of each ball. Apply the two situations that are given in the question to get two equations. These two equations can be solved together to get the value of two variables.

In this question, we are given that 7 bats and 6 balls had cost Rs. 3800 and 3 bats and 5 balls had cost Rs. 1750. We are required to find the cost for each bat and each ball.
Let us assume that each bat had a cost of Rs. x and each ball had a cost of Rs. y.
It is given that 7 bats and 6 balls had cost Rs. 3800. So, we can write,
$7x+6y=3800............\left( 1 \right)$
Also, it is given that 3 bats and 5 balls had cost Rs. 1750. So, we can write,
$3x+5y=1750...........\left( 2 \right)$
By solving these two equations simultaneously, we can find x and y. Multiplying equation $\left( 1 \right)$ by 3 and equation $\left( 2 \right)$ by 7, we get,
$21x+18y=11400............\left( 3 \right)$
$21x+35y=12250............\left( 4 \right)$
Subtracting the above two equations, we get,
$\begin{align}
  & \left( 21x+35y \right)-\left( 21x+18y \right)=12250-11400 \\
 & \Rightarrow 17y=850 \\
 & \Rightarrow y=50 \\
\end{align}$
Substituting y=50 in equation $\left( 1 \right)$, we get,
$\begin{align}
  & 7x+6\left( 50 \right)=3800 \\
 & \Rightarrow 7x+300=3800 \\
 & \Rightarrow 7x=3500 \\
 & \Rightarrow x=500 \\
\end{align}$
Hence, the cost of each bat is equal to Rs. 500 and each ball is equal to Rs. 50.

Note: To check whether we have got the correct answer or not, just substitute the obtained values of x and y in any of the equation $\left( 1 \right)$ and equation $\left( 2 \right)$. If the obtained value of x and y satisfies the equation, we have obtained a correct value of x and y.
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