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.
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.
Sorry!, This page is not available for now to bookmark.