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

1.	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» 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:- ${\pmb{\sf{ 7x+6y = 3800 \ \ \ \ \ \ \ \cdots(<klux>1</klux>) }}} \\ {\pmb{\sf{ 3x+5y = 1750 \ \ \ \ \ \ \ \cdots(<klux>2</klux>) }}} \\$ ✮ 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 $\colon\implies{\sf{ \cancel{-} \ 17y = \cancel{-} \ 850 }} \\ \\ \\ \colon\implies{\sf{ \cancel{17} y = \cancel{850} }} \\ \\ \\ \colon\implies{\sf{ y = <klux>50</klux> }} \\$ 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

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»

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:-

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

✮ 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

$\colon\implies{\sf{ \cancel{-} \ 17y = \cancel{-} \ 850 }} \\ \\ \\ \colon\implies{\sf{ \cancel{17} y = \cancel{850} }} \\ \\ \\ \colon\implies{\sf{ y = <klux>50</klux> }} \\$

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

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

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