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.
Solution: 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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