Question

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

Given

• 7 bats and 6 balls for Rs.3800
• 3 bats and 5 balls for Rs.1750

Explanation

Let the Price of a bat be x and Price of a ball be y as:

✮According to Question,

The Equations be like as:-

${\pmb{\sf{ 7x+6y = 3800 \ \ \ \ \ \ \ \cdots(1) }}} \\ {\pmb{\sf{ 3x+5y = 1750 \ \ \ \ \ \ \ \cdots(2) }}}$

✮ Now, We have to Equalise both Equations as to compare ,We have to Multiply Eq.(1) with 3 and Eq.(2) with 7 so We've :-

$\circ {\boxed{\sf{ 21x+18y = 11400 \ \ \ \ \ \ \ \cdots(1) }}} \\ \\ \circ {\boxed{\sf{ 21x+35y = 12250 \ \ \ \ \ \ \ \cdots(2) }}}$

✮ Now, We can Equalising both Equations;

$\begin{cases} {\pmb{\sf{ \ \ \cancel{21x} +18y = 11400 }}} \\ {\pmb{\sf{ \cancel{ - 21x} -35y = -12250 }}} \\ \\ {\pmb{\boxed{\sf{ \ \ \ -17y = -850}}}} \\ \end{cases}$

✮After Calculating, we've

$\colon\implies{\sf{ \cancel{-} \ 17y = \cancel{-} \ 850 }} \\ \\ \\ \colon\implies{\sf{ \cancel{17} y = \cancel{850} }} \\ \\ \\ \colon\implies{\sf{ y = 50 }}$

Therefore, Price of a ball is ₹50 /Piece.

✮Now, By Putting value of y in any equation to get the value of ' x ' as:-

$\colon\implies{\sf{ 7x+6y = 3800 }} \\ \\ \\ \colon\implies{\sf{ 7x+ 6 \times 50 = 3800 }} \\ \\ \\ \colon\implies{\sf{ 7x + 300 = 3800 }} \\ \\ \\ \colon\implies{\sf{ 7x = 3800-300}} \\ \\ \\ \colon\implies{\sf{ 7x = 3500 }} \\ \\ \\ \colon\implies{\sf{ x = \cancel{ \dfrac{3500}{7} } }} \\ \\ \\ \colon\implies{\sf\purple{ x = Rs. \ 500 }}$

Hence,

• Cost of a Bat is ₹ 500
• Cost of a Ball is ₹ 50