Question

The cost of $2$ kg of apples and $1$ kg of grapes on a day was found to be Rs. $160$. After 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 the cost of 1 kg apples be "x" and 1 kg grapes be "y"

Given that,

$2x+y=160$

$\Rightarrow$ $2x+y-160=0$ ----(1)

and

$4x+2y=300$

$2(2x+y=150)$

$\Rightarrow$ $2x+y-150=0$-----(2)

from equation (1)

$y=160-2x$

when

$x=60$

$y=160-2\times 120=160-120$

$\Rightarrow$ $y=40$

$\therefore x=0$ $\Rightarrow$ $y=40$

when

$x=50$

$y=160-2\times 50=160-100$

$\Rightarrow$ $y=60$

$\therefore x=50$ $\Rightarrow$ $y=60$

So $(60,40)and(50,60)$

from equation (2)

$y=150-2x$

when

$x=60$

$y=150-2\times 120=30$

$\Rightarrow$ $y=300$

$\therefore x=0$ $\Rightarrow$ $y=30$

when

$x=50$

$y=160-2\times 50=150-100$

$\Rightarrow$ $y=50$

$\therefore x=50$ $\Rightarrow$ $y=50$

So $(60,30)and(50,50)$

Above image is the geometrical representation of the solution