Question

3. Romila went to a stationary shop and purchased 2 pencils and 3 erasers for Rs 9. Her friend Sonali saw the new variety of pencils and erasers with Romila and she also bought 4 pencils and 6 erasers of the same kind for Rs 18. Find the cost of each pencil and each eraser.

Standard:- 10

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Answer 1

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:

$2x+3y=9$

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
$2x+3y=9 \\ \\ \implies 2(3) + 3y = 9 \\ \\ \implies 3y = 9-6 \\ \\ \implies 3y = 3 \\ \\ \implies y = 1$

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
Purva
Brainly Community

Answer 2

Answer:

Step-by-step explanation:

Answer

Let the cost of one pencil = Rs x

and cost of one eraser = Rs y

Romila spent = Rs. 9

Sonali spent = Rs. 18

According to the question

2x + 3y = 9 …(1)

4x + 6y = 18 …(2)

Now, table for 2x + 3y = 9

Now, table for 4x + 6y = 18

On plotting points on a graph paper and join them to get a straight line representing 2x + 3y = 9.

Similarly, on plotting the points on the same graph paper and join them to get a straight line representing 4x + 6y = 18.

Here, we can see that both the lines coincide. This is so, because, both the equations are equivalent, i.e.2(2x + 3y) = 2×9 equation (2) is derived from the other.