Question

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

Answer 1

Let Cost of 1 bat=₹x

Let Cost of 1 ball=₹y

Now 7 bats and 6 balls cost ₹3800

Cost of 7 bats=₹7x

Cost of 6 balls=₹6y

$7x + 6y = 3800 \\ \\ 7x = 3800 - 6y \\ \\ x = \frac{3800 - 6y}{7}$

Now 3 bats and 5 balls cost=₹1750

Cost of 3 bats=₹3x

Cost of 5 balls=₹5y

$3x + 5y = 1750 \\ \\ x = \frac{3800 - 6y}{7} \\ \\ 3( \frac{3800 - 6y}{7} ) + 5y = 1750 \\ \\ \frac{11400}{7} - \frac{18y}{7} + 5y = 1750 \\ \\ - \frac{18y}{7} + 5y = 1750 - \frac{11400}{7} \\ \\ \frac{ - 18y + 5y \times 7}{7} = \frac{1750 \times 7 - 11400}{7} \\ \\ \frac{ - 18y + 35 y }{7} = \frac{12250 - 11400}{7} \\ \\ \frac{17y}{7} = \frac{850}{7} \\ \\ y = \frac{850}{7} \times \frac{7}{17} \\ \\ y = 50$

Y=50

We know

3x+5y=1750

3x+5×50=1750

3x+250=1750

3x=1750-250

3x=1500

x=1500/3

x=500

Y is cost of 1 ball=₹50

X is cost of 1 bat=₹500

$\boxed{\mathbf{\huge{Bat=Rs.500}}}$

$\boxed{\mathbf{\huge{Ball=Rs.50}}}$

Answer 2

Let Cost of 1 bat=₹x

Let Cost of 1 ball=₹y

Now 7 bats and 6 balls cost ₹3800

Cost of 7 bats=₹7x

Cost of 6 balls=₹6y

\begin{lgathered}7x + 6y = 3800 \\ \\ 7x = 3800 - 6y \\ \\ x = \frac{3800 - 6y}{7}\end{lgathered}

7x+6y=3800

7x=3800−6y

x=

7

3800−6y

Now 3 bats and 5 balls cost=₹1750

Cost of 3 bats=₹3x

Cost of 5 balls=₹5y

\begin{lgathered}3x + 5y = 1750 \\ \\ x = \frac{3800 - 6y}{7} \\ \\ 3( \frac{3800 - 6y}{7} ) + 5y = 1750 \\ \\ \frac{11400}{7} - \frac{18y}{7} + 5y = 1750 \\ \\ - \frac{18y}{7} + 5y = 1750 - \frac{11400}{7} \\ \\ \frac{ - 18y + 5y \times 7}{7} = \frac{1750 \times 7 - 11400}{7} \\ \\ \frac{ - 18y + 35 y }{7} = \frac{12250 - 11400}{7} \\ \\ \frac{17y}{7} = \frac{850}{7} \\ \\ y = \frac{850}{7} \times \frac{7}{17} \\ \\ y = 50\end{lgathered}

3x+5y=1750

x=

7

3800−6y

3(

7

3800−6y

)+5y=1750

7

11400

−

7

18y

+5y=1750

−

7

18y

+5y=1750−

7

11400

7

−18y+5y×7

=

7

1750×7−11400

7

−18y+35y

=

7

12250−11400

7

17y

=

7

850

y=

7

850

×

17

7

y=50

Y=50

We know

3x+5y=1750

3x+5×50=1750

3x+250=1750

3x=1750-250

3x=1500

x=1500/3

x=500

Y is cost of 1 ball=₹50

X is cost of 1 bat=₹500