Question

5 pencils &7 pens together cost Rs.50 whereas 7 pencils & 5 pens together costs Rs. 46.find the cost of one pen & one pencil 

Answer 1

Let pencil be x and let pen be y
5x+7y=50
7x+5y=46
multiply first equation by 7
35x+49y = 350
multiply second equation by 5
35x+25y=230
solving them we get 24y=120 which gives y is 5 rupees
substituting in second equation we get x is 3 rupees

Answer 2

5 pencils &7 pens together cost Rs.50 whereas 7 pencils & 5 pens together costs Rs. 46.find the cost of one pen & one pencil

Solution:
             let cost(in RS) of one pencil = x
             and cost (in RS) of one pen = y
Therefore , according to question
                      5x+7y = 50  ........ (1)
                     7x + 5y = 46  .........(2)
       Multiply equation 1 by 7 and equation by 5 we get
                         7(5x+7y)= 7*50
                         35x +49y = 350 .......(3)
                   and
                         5(7x +5y) = 5*46
                         35x +25y = 230 ....... (4)

Subtract equation 4 from equation 3 , we get
                            35x + 49y - 35x - 25y = 350 -230
                             49y -25y = 120
                             24y = 120
                                 y = 120 /24
                                 y= 5
Substitute y=5 in equation 1 , we get
                 5x +  7*5 =50
                 5x+35 =50
                 5x = 50 - 35
                 5x =15
                 x= 15/5
                 x=3

Hence Cost of One Pencil = x =3
           Cost  of One Pen =y =5

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