Question

(i) 5 pencils and 7 pens together cost 50, whereas 7 pencils and 5 pens together
cost * 46. Find the cost of one pencil and that of one pen.​

Answer 1

Answer:

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

Another method

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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