Question

Romila went to a stationery shop and purchased 2 pencils and 3 erasers for 9/- . Her friend Sonali saw the new variety of pencils and erasers with Romali and she also bought 4 pencils and 6 erasers of the same kind for 18/- . Represent this situation algebraically and graphically.

Answer 1

Hint: For these kinds of questions , we have to use variables. Since we have only two quantities , namely pens and pencils , we need only 2 variables. And then we have to form equations according to each girl and then plot their graph. We just have to represent the given information mathematically.

Complete step-by-step solution:
So Romila has 2 pencils and 3 erasers.
And her friend Sonali has 4 pencils and 6 erasers.
So let the cost of 1 pencil be named the variable $x$ .
And let the cost of 1 eraser be named the variable $y$ .
From the question , let us construct an equation with the given data.
Romila has 2 pencils which means $2x$ and she has 3 erasers which means $3y$ .
She bought these pencils and erasers together for 9/-. So the equation for this becomes $2x+3y=9$ .
And in the same way, her friend , Sonali has 4 pencils which means $4x$ and she has 6 erasers which means $6y$ .
She bought these pencils and erasers together for 18/-. So the equation for this becomes $4x+6y=18$.
 So now we got both the equations.
Now let us graph them.

We see only the line. It is because $4x+6y=18$ can be reduced to $2x+3y=9$ when it is divided by 2.
$\therefore $ Hence the equations which represent the purchases of Romila and her friend Sonali is $2x+3y=9$ and $4x+6y=18$ respectively.

Note: For these kinds of questions , the first and foremost thing we need is to check the number of quantities mentioned in the question. Then only we can decide the number of variables we have to consider. We have to be careful while constructing the equation. Plotting also must be done with care.