5 PENCILS and 7 PENS together Cost Rs. 50, Whereas 7 Pencils and 5 Pens together Cost Rs. 46. Find the Cost of One Pencil and that of One pen by Graphical Method | Bzziii.com

5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen by graphical method.

Let the Cost of one pencil be Rs x

and Cost of one Pen be Rs y

Given that,

5 Pencils and 7 Pens together cost Rs 50

5 `\times` (Cost of Pencils) + 7 `\times` (Cost of Pens) = 50

5x + 7y = 50     .....(1)

Also, 7 Pencils and 5 Pens together cost Rs. 46

7 `\times` (Cost of Pencils) + 5 `\times` (Cost of Pens) = 46

7x + 5y = 46     .....(2)

Now, Plotting equations,

5x + 7y = 50     .....(1)

7x + 5y = 46     .....(2)

Now, for equation (1)

5x + 7y = 50

x	3	0
y	5	7.14

Let y = 5 

 5x + 7y = 50 

5x + 7(5) = 50

5x + 35 = 50

5x = 50 - 35

5x = 15x = `15/5`

So, x = 3, y = 5 is a solution i.e. (3,5) is a solution

Let x = 0 5x + 7y = 505(0) + 7y = 50

0 + 7y = 50

7y = 50

y = `50/7`

So, x = 0, y = 7.14 is a solution i.e. (0,7.14) is a solution

Now, for equation (2)

7x + 5y = 46

x	6.57	3
y	0	5

Let y = 0

7x + 5y = 46

7x + 5(0) = 46

7x + 0 = 46

7x = 46

x = `46/7`

x = 6.57

So, x = 6.57, y = 0 is a solution i.e. (6.57,0) is a solution

Let x = 3 

7x + 5y = 46

 7(3)  + 5y = 46

21 + 5y = 46

5y = 46 - 21

5y = 25

y = `25/5`

y = 5

So, x = 3, y = 5 is a solution i.e. (3,5) is a solution

Now, we will plot both equations on the graph

Thus, Cost of 1 Pencil = x = Rs. 3

and, Cost of 1 Pen = y = Rs. 5