Question 1 (ii). 5 Pencils and 7 Pens Together Cost Rs 50, Wherea Exercise 3.2 Chapter 3 Pair of Linear Equations in

Question 1 (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 cost of pencil      = Rs x
Cost of pens             = 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 – 7 y
Divide by 5 we get
X         = 10  - 7 y /5
Plug value of y which is factor of 5 to get whole number so plug y = 5 , 10  and 15 we get
X         = 10 – 7 * 5 / 5           =  10 – 7        = 3
X         = 10 – 7 * 10 / 5         =  10 – 14       = - 4
X         = 10 – 7 * 15 / 5        = 10 – 21        = - 11

Given that 7 pencils and 5 pens together cost Rs 46
7  x + 5 y       = 46
Subtract 7x both side we get
5y        = 46 – 7x
Divide by 5 we get
Y         = 46 / 5   - 7 x / 5
Y         = 9.2 – 1.4  x
Plug x  = 0 , 2 and 4 we get
Y         =  9.2 – 1.4 * 0           =  9.2 – 0        = 9.2
Y         =  9.2 – 1.4 (2)           = 9.2 – 2.8      =6.4
Y         =  9.2 – 1.4 (4)           = 9.2 – 5.6      = 3.6

  Answer  cost of 1 pencil = Rs 3 Cost of 1 pen = Rs 5