Thahini bought some pencils and erasers. Her friend Ashwin spent the same amount and bought thrice as many pencils and five less erasers. Now they are all set to start their group study for V.O.T.E. If the cost of 1 eraser is 2 more than the cost of 1 pencil, then what is the minimum possible number of pencils bought by Thahini and Ashwin together?​

Step-by-step explanation:

Let the COST of one pencil = Rs. x

Let the cost of one ERASER = Rs. y

Romila purchases 2 pencils and 3 erasers for Rs. 9 

Cost of 2 pencils = 2x

Cost of 3 erasers = 3y

Total Cost = Rs. 9

So, we have:

2x + 3y = 9 ---(1)

Sonali purchases 4 pencils and 6 erasers for Rs 18. 

Cost of 4 pencils = 4x

Cost of 6 erasers = 6y

Total Cost = 18

So, we have:

4x + 6y = 18

So, 2(2x + 3y) = 18

So, 2x + 3y = 9 ----(2)

Here, we see that both (1) and (2) are the same equation, which is:

2x+3y=92x+3y=9

This single equation has INFINITELY Many Solutions, as it is a linear equation in two variables. 

We can PUT any value of x, and find the CORRESPONDING value of y. 

However, since x and y refer to Costs, we can only take positive values. We still can have infinite solutions.

For example, 

If Cost of 1 pencil = Rs. 3 = x

Then

\begin{gathered}2x+3y=9 \\ \\ \implies 2(3) + 3y = 9 \\ \\ \implies 3y = 9-6 \\ \\ \implies 3y = 3 \\ \\ \implies y = 1\end{gathered}2x+3y=9⟹2(3)+3y=9⟹3y=9−6⟹3y=3⟹y=1

So, If Cost of one pencil = Rs. 3,

Then Cost of one eraser = Rs. 1

Similarly, we can take other values of one variable, and find corresponding values of other variable.

Hope it helps

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