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.
Last updated date: 19th Mar 2023
•
Total views: 304.8k
•
Views today: 8.85k
Answer
304.8k+ views
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.
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
