5 Pencils and 7 Pen together cost Rs.50, whereas 7 Pencils and 5 Pens together cost Rs.46.

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Q1.(ii) 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.

Solution:            

  Let be pencil cost = X Rs

  Let be pen cost = Y Rs

  5 Pencils and 7 Pens together cost = Rs.50

   5X + 7 Y = 50 ----------------(1)

  7 Pencils and 5 Pens together cost = Rs.46

   7X + 5Y = 46 ----------------(2)

  Let we take equation (1)               

      5X + 7 Y = 50

      7Y = 50-5X

       Y = 50-5X/7

       Y = 50-5(-3)/7

         = 50+15/7=35/7=5

       Y = 50-5(-4)/7

         = 50+20/7=70/7=10

       Y = 50-5(10)/7

         = 50-50/7=0/7=10

Table

X  3 -4 10
Y=50-5X/7     5     10      0
(X,Y)   (3,5)  (-4,10)   (10,0)


Let we take equation (2)               
 7X + 5Y = 46
         5Y = 46-7X
          Y = 46-7X/5
          Y = 46-7(3)/5
            = 46-21/5=25/5=5
          Y = 46-7(-2)/5
            = 46+14/5=60/5=12
          Y = 46-7(8)/5
            = 46-56/5=-10/5=-2

Table
X  3 -2   8
Y=46-7X/5     5      12         -2
(X,Y)     (3,5)    (-2,12)    (8,-2)

Graphically Solving (Plotting points on Graph page)

Intersect Point (X,Y) = (3,5)

Pencil Cost (X) = Rs.3

Pen Cost (Y) = Rs.5







Post details 

CBSE Class 10 Maths

Name of Chapter: Pair of Linear Equations in Two Variables

Chapter : 3

Exercise : 3.1

Question Number 1.(ii)

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