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

x30
y57.14
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

x6.573
y05
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

5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46


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

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



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