Question

Question 3
The cost of 2 kg of apples and 1kg 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

Let cost each kg of apples = Rs x
Cost of each kg of grapes = Rs y
Given that the cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160.
So,
2 x + y = 160 … (i)
2x = 160 - y
$x=\frac{(160-y)}{2}$
Let y = 0 , 80 and 160, we get,
$x=\frac{160-0}{2}=80$
$x=\frac{(160-80)}{2}=40$
$x=\frac{160-2\times 80}{2}=0$
$\begin{array}{cccc}x& 80& 40& 0\\ y& 0& 80& 160\end{array}$
Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300.
So, we get;
4x + 2y = 300 … (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 … (i)
4x + 2y = 300 … (ii)
Graphical representation: