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

Question : The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. Later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball.

Doubt by Gurpreet 

Solution : 

Let the cost of each bat = ₹ x
and the cost of each ball = ₹ y

ATQ
7x+6y=3800 — (1)
3x+5y=1750 — (2)

Using equation (1)
7x = 3800 - 6y
x = (3800 - 6y) / 7 — (3)

Putting in equation (2)

3((3800 - 6y) / 7) + 5y = 1750
(11400 - 18y) / 7 + 5y = 1750
11400 - 18y + 35y = 1750 ×7
11400 + 17y = 12250
17y = 12250 - 11400
17y = 850
y = 850 / 17
y = 50

Putting in equation (3)
x = (3800 - 6y) / 7
x = (3800 - 6×50) / 7
x = (3800 - 300) / 7
x = 3500 / 7
x = 500

Hence,

the cost of each bat = ₹ 500 
and the cost of each ball = ₹ 50.