Cost of an Audio Cassette and a Video Cassette

Video Explanation

Question

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 one audio cassette and one video cassette.

Solution

Step 1: Let the Variables

Let the cost of one audio cassette = Rs \(x\)

Let the cost of one video cassette = Rs \(y\)

Step 2: Form the Equations

\[ 7x + 3y = 1110 \quad (1) \]

\[ 5x + 4y = 1350 \quad (2) \]

Step 3: Solve by Elimination Method

Multiply equation (1) by 4:

\[ 28x + 12y = 4440 \quad (3) \]

Multiply equation (2) by 3:

\[ 15x + 12y = 4050 \quad (4) \]

Subtract (4) from (3):

\[ 13x = 390 \]

\[ x = 30 \]

Step 4: Find the Value of y

Substitute \(x = 30\) in equation (1):

\[ 7(30) + 3y = 1110 \]

\[ 210 + 3y = 1110 \]

\[ 3y = 900 \]

\[ y = 300 \]

Conclusion

Cost of one audio cassette:

\[ \boxed{Rs\;30} \]

Cost of one video cassette:

\[ \boxed{Rs\;300} \]