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 Rd.1750. Find the cost of each bat and each ball .



solve by substitution method

brainlist answers for valid answer ​

Answer 1

solution:

let the cost of the each bat be=Rs x

let the cost of the each ball be=Rs y

=> 7x + 6y =3800

=>6y =3800 - 7x

Dividing by 6,we get

=> y =(3800-7x)/6

(1) 3x+5y=1750

putting the value of y

=>3x+5[(3800-7x)/6] = 1750

multiplying by 6,we get

=>18 x 19000 - 35x = 10500

=> -17x = 10500 - 19000

=> -17x = - 8500

=> x = - 8500/-17

=> x = 500

putting this value in equation (1) we get

=> y = (3800 -7 × 500)/6

=> y =300/6

=> y = 50

Hence, the cost of each bat is =Rs 500 and the cost of each ball is = Rs 50

Answer 2

Given :

• The coach of a cricket team buys 7 bats and 6 balls for Rs.3800.
• Also, she buys 3 bats and 5 balls for Rs.1750.

To Find :

• Cost of each bat and each ball.

Solution :

Let the cost of bat be ₹ x.

Let the cost of ball be ₹ y.

Case 1 :

Cost of 7 bats and 6 balls is 3800.

✪ Equation :

$\longrightarrow$ $\mathtt{7x+6y=3800}$

$\longrightarrow$ $\mathtt{7x\:=\:3800-6y}$

$\mathtt{x\:=\:{\dfrac{3800-6y}{7}}}$ ____(1)

Case 2 :

Cost of 3 bats and 5 balls is ₹ 1750.

✪ Equation :

$\longrightarrow$ $\mathtt{3x+5y=1750}$

✪ Substite value of x from equation 1,

$\longrightarrow$ $\mathtt{3\:\times\:{\dfrac{3800-6y}{7}\:+\:5y\:=\:1750}}$

$\longrightarrow$ $\mathtt{\dfrac{11400\:-18y}{7}\:+\:5y\:=\:1750}$

$\longrightarrow$ $\mathtt{\dfrac{11400-18y\:+\:35y}{7}\:=\:1750}$

$\longrightarrow$ $\mathtt{\dfrac{11400+17y}{7}\:=\:1750}$

$\longrightarrow$ $\mathtt{11400\:+\:17y\:=\:12250}$

$\longrightarrow$ $\mathtt{17y\:=\:12250-11400}$

$\longrightarrow$ $\mathtt{17y\:=\:850}$

$\longrightarrow$ $\mathtt{y\:={\dfrac{850}{17}}}$

$\longrightarrow$ $\mathtt{y=50}$

✪ Substitute y = 50 in equation 1,

$\longrightarrow$ $\mathtt{x\:=\:{\dfrac{3800-\:6\:\times\:50}{7}}}$

$\longrightarrow$ $\mathtt{x\:=\:{\dfrac{3800-300}{7}}}$

$\longrightarrow$ $\mathtt{x\:=\:{\dfrac{3500}{7}}}$

$\longrightarrow$ $\mathtt{x\:=\:500}$

$\large{\boxed{\tt{\red{Cost\:of\:each\:bat\:=\:x\:=\:Rs.500}}}}$

$\large{\boxed{\tt{\red{Cost\:of\:each\:ball\:=\:y\:=\:Rs.50}}}}$