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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Solution
Let the cost of the bat and a ball be x and y respectively
According to the given information
7x + 6y = 3800 ...(1)
3x + 5y = 1750 ....(2)
From (1), we obtain
y = `(3800 - 7x)/6` ....(3)
Substituting this value in equation (2), we obtain
`3x + 5((3800 - 7x)/6) = 1750`
`3x + 9500/3 - (35x)/6 = 1750`
`3x - (35x)/6 = 1750 = 9500/3`
`3x - (35x)/6 = (5250 - 9500)/3`
`-(17x)/6 = (-4250)/3`
`-17x = -8500`
x = 500 ...(4)
Substituting this in equation (3), we obtain
`y = (3800 - 7 xx 500)/6`
`= 300/6 = 50`
Hence, the cost of a bat is Rs 500 and that of a ball is Rs 50.
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