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

Given:

7 audio cassettes and 3 video cassettes cost ₹ 1110, while 5 audio cassettes and 4 video cassettes cost ₹ 1350.

To do:

We have to find the cost of an audio cassette and a video cassette.

Let the cost of an audio cassette and a video cassette be $x$ and $y$ respectively.

According to the question,

$7x + 3y = 1110$.....(i)

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

Multiplying equation (i) by 4 on both sides, we get,

$4(7x+3y)=4(1110)$

$28x+12y=4440$.....(iii)

Multiplying equation (ii) by 3 on both sides, we get,

$3(5x+4y)=3(1350)$

$15x+12y=4050$.....(iv)

Subtracting equation (iv) from equation (iii), we get,

$(28x+12y)-(15x+12y)=4440-4050$

$28x-15x+12y-12y=390$

$13x=390$

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

$x=30$

Substituting $x=30$ in equation (ii), we get,

$5(30)+4y=1350$

$150+4y=1350$

$4y=1350-150$

$4y=1200$

$y=\frac{1200}{4}$

$y=300$

$x=30$ and $y=300$

The cost of an audio cassette is Rs. 30 and the cost of a video cassette is Rs. 300.