
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Represent the situation algebraically and graphically.
A. \[\begin{align}
& 2x+y=160\text{ } \\
& 4x+2y=300 \\
\end{align}\]
B. \[\begin{align}
& x+2y=160\text{ } \\
& 4x+2y=300 \\
\end{align}\]
C. \[\begin{align}
& x+2y=160\text{ } \\
& 2x-4y=300 \\
\end{align}\]
D. None of these
Answer
584.7k+ views
Hint: Find the equations from the given conditions to represent the situation algebraically. Then plot the two curves of those two equations to represent the situation graphically. Assume that the cost of 1 kg of apples is Rs. x and 1 kg grapes is Rs. y . There will be two different equations from the two given conditions.
Complete step-by-step answer:
In the question, we are given that the cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300.
So here to represent the two situations algebraically, we have to find two equations in terms of the two variables x and y. Now here assume that the cost of 1 kg of apples is Rs. x and 1 kg grapes is Rs. y .
So here, in situation 1, it is given that the cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. So the cost of 2 kg of apples is given as Rs 2x and the cost of 1 kg of grapes is Rs y.
Also, the total is Rs 160, so in the equation form, we will get: \[2x+y=160\text{ }\].
Again, it is given that the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. So the cost of 4 kg of apples is given as Rs 4x and the cost of 2 kg of grapes is Rs 2y.
Now again here the total is Rs 300, so in the equation form, we will get: \[4x+2y=300\].
So combining the two situations, we get:
\[\begin{align}
& 2x+y=160\text{ } \\
& 4x+2y=300 \\
\end{align}\]
And hence this is the algebraic representation.
Hence Option A is correct.
Now, for the graphical representation, we need to use the graphic utility and will plot the two equations as shown below:
So here the red curve is \[4x+2y=300\] and the blue curve is \[2x+y=160\text{ }\]
Note: Care has to be taken while simplifying the finding the total cost. Here, we are not required to find the cost of apples and grapes but just have to represent the situation algebraically and graphically. The two lines are parallel and hence do not have intersection points.
Complete step-by-step answer:
In the question, we are given that the cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300.
So here to represent the two situations algebraically, we have to find two equations in terms of the two variables x and y. Now here assume that the cost of 1 kg of apples is Rs. x and 1 kg grapes is Rs. y .
So here, in situation 1, it is given that the cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. So the cost of 2 kg of apples is given as Rs 2x and the cost of 1 kg of grapes is Rs y.
Also, the total is Rs 160, so in the equation form, we will get: \[2x+y=160\text{ }\].
Again, it is given that the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. So the cost of 4 kg of apples is given as Rs 4x and the cost of 2 kg of grapes is Rs 2y.
Now again here the total is Rs 300, so in the equation form, we will get: \[4x+2y=300\].
So combining the two situations, we get:
\[\begin{align}
& 2x+y=160\text{ } \\
& 4x+2y=300 \\
\end{align}\]
And hence this is the algebraic representation.
Hence Option A is correct.
Now, for the graphical representation, we need to use the graphic utility and will plot the two equations as shown below:
So here the red curve is \[4x+2y=300\] and the blue curve is \[2x+y=160\text{ }\]
Note: Care has to be taken while simplifying the finding the total cost. Here, we are not required to find the cost of apples and grapes but just have to represent the situation algebraically and graphically. The two lines are parallel and hence do not have intersection points.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
Name the states through which the Tropic of Cancer class 8 social science CBSE

Full form of STD, ISD and PCO

What are gulf countries and why they are called Gulf class 8 social science CBSE

Which place in Tamil Nadu is known as Little Japan class 8 social science CBSE

Advantages and disadvantages of science

India has the largest road network in the world A First class 8 social science CBSE


