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

Let’s assume the cost of an audio cassette and that of a video cassette be ₹a and ₹b, respectively. Then forming equations according to the question, we have

$7a+3b=1110$…(a)

$5a+4b=1350$… (b)

On multiplying equation (a)$bb4$ and equation (b)bb3,

We get,

$28a+12b=4440$…(c)

$15a+4b=4050$…(d)

Subtracting equation (iv) from equation (c),

$28a–13a+12b–12b=4440–4050$

$13a=390$

⇒a$=30$

On substituting $a=30$ in equation (a)

$7(30)+3b=1110$

$3b=1110–210$

$b=900/3$

⇒b$=300$

Therefore, it’s found that the cost of one audio cassette $=₹30$

And the cost of one video cassette $=₹300$