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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.
Solution: 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.