Question

Seven audio cassettes and three video cassettes cost Rs.1110, while five audio cassettes and 4 video cassettes costs Rs.1350. Find the cost of audio cassettes and video cassettes.

Answer 1

Hint:- Form a set of linear equations by using the given data. Use elimination method to solve this system of two equations and two unknowns.

Given , 7 audio cassettes & 3 video cassettes together costs Rs.1110 and 5 audio cassettes and 4 video cassettes together costs Rs.1350. We need to find the cost of the audio cassette and the video cassette.
Let, the cost of one audio cassette and video cassette be A and B respectively.
Now, according to the question,
7A + 3B =1110 -(1)
5A + 4B = 1350 -(2)
For finding the cost of one cassette of each type , we need to solve equation (1) and (2).
We have two equations and two unknowns. To solve these equations , we are going to use elimination by multiplication method i.e. we will multiply both equations with constants such that coefficients of either A or B becomes equal.
Multiplying Equation (1) with 5 and Equation(2) with 7 , we get
35A + 15 B = 5550 -(3)
35A + 28B =9450 -(4)
Now, we have coefficients of A equal in both the equations. On subtracting equation (4) from equation(3), we can get the value of B.
Subtracting Equation (4) from Equation(3),
28B – 15B = 9450-5550
13B=3900
B=300
Substitution the value of B in equation (1), we get
7A + 3(300) =1110
7A +900 = 1110
7A =210
A=30
Hence, A = 30 and B=300 i.e. the cost of one audio cassette is Rs.30 and cost of one video cassette is Rs. 300.

Note:- In these types of questions, there can be different ways to solve. For solving a system of equations of unknown variables , there are two basic methods. Method 1 is Substitution method and Method 2 is Elimination by multiplication method.