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.

Given:

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. 

To do:

We have to find the cost of each bat and each ball.

Let the cost of one bat and one ball be $x$ and $y$ respectively.

According to the question,

$7x + 6y = 3800$.....(i)

$3x + 5y = 1750$.....(ii)

Multiplying equation (i) by 5 on both sides, we get,

$5(7x+6y)=5(3800)$

$35x+30y=19000$.....(iii)

Multiplying equation (ii) by 6 on both sides, we get,

$6(3x+5y)=6(1750)$

$18x+30y=10500$.....(iv)

Subtracting equation (iv) from equation (iii), we get,

$(35x+30y)-(18x+30y)=19000-10500$

$35x-18x+30y-30y=8500$

$17x=8500$

$x=\frac{8500}{17}$

$x=500$

Substituting $x=500$ in equation (ii), we get,

$3(500)+5y=1750$

$1500+5y=1750$

$5y=1750-1500$

$5y=250$

$y=\frac{250}{5}$

$y=50$

The cost of each bat is Rs. 500 and the cost of each ball is Rs. 50.   

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Updated on: 10-Oct-2022

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