Question

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.

Answer 1

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.