Question

The cost of $2kg$ of apples and $lkg$ of grapes on a day was found to be Rs 160. After a month, the cost of $4kg$ of apples and $2kg$ of grapes is $Rs300$. Represent the situation algebraically and geometrically.

Answer 1

Let cost each $kg$ of apples $=Rsx$
Cost of each $kg$ of grapes $=$ Rs $y$
Given that the cost of $2kg$ of apples and $1kg$ of grapes on a day was found to be Rs 160 .
So,
$$2x+y=160\dots \text{(i)}$$
$$\begin{array}{cc}& 2x=160-y\\ & x=\frac{(160-y)}{2}\end{array}$$
Let $y=0,80$ and 160, we get, $x=\frac{160-0}{2}=80$
$$\begin{array}{cc}& x=\frac{(160-80)}{2}=40\\ & x=\frac{160-2\times 80}{2}=0\end{array}$$
$$\begin{array}{cccc}x& 80& 40& 0\\ y& 0& 80& 160\end{array}$$
Given that the cost of $4kg$ of apples and $2kg$ of grapes is Rs 300 .
So, we get;
$$4x+2y=300\text{... (ii)}$$
Dividing by 2 we get,
$$2x+y=150$$
Subtracting $2x$ both side, we get, $y=150-2x$
Putting $x=0,50,100$ we get,
$y=150-2\times 0=150$
$$y=150-2\times 50=50$$
$y=150-2\times \left(100\right)=-50$
$$\begin{array}{cccc}x& 0& 50& 100\\ y& 150& 50& -50\end{array}$$
Algebraic representation:
$2x+y=160\dots$.. (i)
$4x+2y=300$... (ii)
Graphical representation: