Question

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 geometrically.

Answer 1

Hint: In this question, we need to assume the cost of kg apples as x and the cost of kg grapes as y. Then from the given conditions in the question, we get the respective algebraic equations which then on converting in terms of any of the one variable helps in geometric representation.

Complete step by step answer:
Let us assume the cost of 1 kg apples as Rs. x and the cost of 1 kg grapes as Rs. y
Now, given that the cost of 2 kg apples and 1 kg grapes is Rs.160
Now, this can be written in terms of the algebraic equation as
\[\Rightarrow 2x+y=160\]
Now, given that the cost of 4 kg apples and 2 kg grapes is Rs.300
Now, this can be written in terms of the algebraic equation as
\[\Rightarrow 4x+2y=300\]
Now, the algebraic representation of the given system is
\[\begin{align}
  & 2x+y=160 \\
 & 4x+2y=300 \\
\end{align}\]
Now, let us write the above both equations in terms of y
\[\Rightarrow y=160-2x\]
\[\Rightarrow y=\dfrac{300-4x}{2}\]
Now, let us find few corresponding values to represent them geometrically

x	50	60	70
y	60	40	20

x	40	50	60
y	70	50	30

Now, plot these points to represent the situation geometrically

Here, we can observe that both the lines do not intersect each other and are parallel so they do not have a common solution which means they have no unique solution.
This shows the prices are different
Note:
Instead of finding the equations in terms of y to represent them geometrically, we can also express them in terms of x and they further consider the values respectively and then represent which also gives the same representation.
It is important to note that the two lines are parallel which means they have a trivial solution and no unique solution. It is also to be noted that while writing the equations we should not neglect any of the terms which change the corresponding equation.