7 audio cassettes and 3 video cassettes cost Rs 1110, while 5 audio cassettes and 4 video cassettes cost Rs 1350. Find the cost of an audio cassette and a video cassette.

Solution:

Given: 

(i) 7 Audio cassettes and 3 Video cassettes cost is 1110.

(ii) 5 Audio cassettes and 4 Video cassettes cost Rs. 1350.

To Find: Cost of 1 audio cassette and 1 video cassettes.

Let (i) the cost of 1 audio cassette = Rs. x.

(ii) the cost of 1 video cassette = Rs. y.

According to the given conditions, we have

$7 x+3 y=1110$

$\Rightarrow 7 x+3 y-1110=0$....(1)

$5 x+4 y=1350$....(2)

$\Rightarrow 5 x+4 y-1350=0$

Thus, we get the following system of linear equation,

$7 x+3 y-1110=0$...(1)

$5 x+4 y-1350=0$....$(2)$

By using cross multiplication, we have

$\frac{x}{-4050-(-4440)}=\frac{-y}{-9450-(-5550)}=\frac{1}{28-15}$

$\frac{x}{-4050+4440}=\frac{-y}{-9450+5550}=\frac{1}{28-15}$

$\frac{x}{390}=\frac{-y}{-3900}=\frac{1}{13}$

$\therefore x=\frac{390}{13}$

$x=$ Rs. 30

$\therefore y=\frac{3900}{13}$

$y=$ Rs. 300

Hence cost of 1 audio cassette $=$ Rs. 30

Hence cost of 1 video cassette $=$ Rs. 300