Question

Form the pair of linear equations for the following problem and find their solution by substitution method.

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.

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

Answer 1

Let the cost of one bat be x rupees

And the cost of one ball is Rs y.

Situation I

7 bats + 6 balls = 3800

⇒ 7x + 6y = 3800            ...(i)

Situation II

3 bats + 5 balls = 1750

⇒ 3x + 5y = 1750              ...(ii)

From equation (ii)

3x + 5y = 1750

⇒ 3x = 1750 – 5y

⇒ x = `(1750 - 5y)/3`

Now on putting this value of x in equation (i)

7x + 6y = 3800

⇒ `7((1750 - 5y)/3) + 6y = 3800`

⇒ 12250 – 35y + 18y = 11400

⇒ 12250 – 17y = 11400

⇒ 17y = 12250 – 11400

⇒ 17y = 850

⇒ y = `850/17`

⇒ y = 50

Now putting y = 50 in equation (ii)

⇒ x = `(1750 - 5y)/3`

⇒ x = `(1750 - 5 xx 50)/3`

⇒ x = `(1750 - 250)/3`

⇒ x = `1500/3`

⇒ x = 500

⇒ x = 500 and y = 50

Hence, the cost of one bat is Rs 500 and the cost of one ball is Rs 50.