Question

The cost of $2kg$ of apples and $1kg$ of grapes on a day was found to be $Rs160$. After a month, the cost of $4kg$ of apples and $2kg$ of grapes is $Rs300$. Represent the situation algebraically and geometrically.

Answer 1

The algebraic representation can be as follows:

Let the cost of $1$ kg of apples be $x$ and that of $1$ kg be $y$

$2x+y=160$
$4x+2y=300\Rightarrow 2x+y=150$

The situation can be represented graphically by plotting these two equations.

$2x+y=160\Rightarrow y=160-2x$

$\begin{array}{ccccc}x& 70& 60& 50& 40\\ y=160-2x& 20& 40& 60& 80\end{array}$

$2x+y=150\Rightarrow y=150-2x$

$\begin{array}{ccccc}x& 65& 55& 45& 35\\ y=150-2x& 20& 40& 60& 80\end{array}$

We can see that the lines do not intersect anywhere, i.e. they are parallel. Hence we can not arrive at a solution.