# The coach of a cricket team buys 7 bats and 6 balls for Rs 3800.

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.

Solution:

Given: (i) 7 bats and 6balls cost is Rs3800

(ii) 3 bats and 5balls cost is Rs1750

To find: Cost of 1 bat and 1 ball

Let (i) the cost of 1 bat = Rs. x.

(ii) the cost of 1 ball = Rs. y.

According to the given conditions, we have

$7 x+6 y=3800$

$7 x+6 y-3800=0$.....(1)

$3 x+5 y=1750$

$3 x+5 y-1750=0$....(2)

Thus, we get the following system of linear equation,

7x + 6y − 3800 = 0 …… (1)

3x + 5y − 1750 = 0 …… (2)

By using cross multiplication, we have

$\frac{x}{(-1750 \times 6)-(-3800 \times 5)}=\frac{-y}{(-1750 \times 7)-(-3800 \times 3)}=\frac{1}{35-18}$

$\frac{x}{(8500)}=\frac{-y}{(-850)}=\frac{1}{17}$

$\frac{x}{(8500)}=\frac{1}{17}$

$x=500$

$\frac{-y}{(-850)}=\frac{1}{17}$

$x=50$

Hence cost of 1 bat $=x=500$

Hence cost of 1 ball $=x=50$