5 pencil and 7 pens together coast rs 50 whereas 7 pencil and 5 pen together cost rs 46 find the cost of one pencil and that of on

2 thoughts on “5 pencil and 7 pens together coast rs 50 whereas 7 pencil and 5 pen together cost rs 46 find the cost of one pencil and that of on”

1. Answer:

   Cost of one pencil = Rs. 3 and that of one pen = Rs. 5

   Step-by-step explanation:

   Let cost of pencil be Rs. x

   Cost of pens be Rs. y

   5 pencils and 7 pens together cost Rs. 50,

   So we get

   5x+7y=50

   Subtract 7y both side we get

   5x=50–7y

   Divide by 5 we get

   x=10−

   5

   7

   y

   Plug value of y which is factor of 5 to get whole number so plug y=5,10,15 we get

   fory=5

   x=10−

   5

   7

   y=10−7=3

   for y=10

   x=10−

   5

   7

   y=10−14=−4

   fory=15

   x=10−

   5

   7

   y=10−21=−11

   Therefore, the required points are (3,5),(−4,10),(−11,15).

   Given that 7 pencils and 5 pens together cost Rs. 46

   7x+5y=46

   Subtract 7x both side we get

   5y=46–7x

   Divide by 5 we get

   y=9.2–1.4x

   Plug x=0,2,4 we get

   for x=0

   y=9.2–0=9.2

   for x=2

   y=9.2–2.8=6.4

   forx=4

   y=9.2–5.6=3.6

   Therefore, the required points are (0,9.2),(2,6.4),(4,3.6).

   The graph is as shown below:

   Since the point of intersection is (3,5),

   Hence, the cost of one pencil is Rs. 3 and the cost of one pen is Rs. 5

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2. Answer :

   • Cost of one pencil is Rs.3
   • Cost of one pen is Rs.5

   Given :

   • 5 pencils and 7 pens together cost rupees 50
   • 7 pencils and 5 pens together cost rupees 46

   To find :

   • Cost of one pencil and one pen

   Solution :

   • Let the cost of one pencil be x
   • Let the cost of pen be y

   According to question ,

   》5x + 7y = 50

   》7x + 5y = 46

   5x + 7y = 50 is eq (1) and 7x + 5y = 46 is eq (2)

   Now , we have to multiply 7 in equation (1) we get ,

   》7 × 5x + 7y = 50

   》35x + 49y = 350

   35x + 49y = 350 is eq (3)

   Now , we have to multiply 5 in equation (2) we get ,

   》5 × 7x + 5y = 46

   》35x + 25y = 230

   35x + 25y = 230 is eq (4)

   Now we have to equation 3 and equation 4 we get ,

   》35x + 49y = 350 – 35x + 25y = 230

   》24y = 120

   》y = 120/24

   》y = 5

   Now Substituting the value of y = 5 in equation (2) we get,

   》7x + 5y = 46

   》7x + 5(5) = 46

   》7x + 25 = 46

   》7x = 21

   》x = 21/7

   》x = 3

   • Cost of one pencil is Rs.3
   • Cost of one pen is Rs.5

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