Question

5 books and 7 pens together cost Rs. 79, while 7 books and 5 pens together cost Rs. 77. What is the cost of 1 book and 2 pens?

Answer 1

Suppose x and y be the  costs of one book and one pen, respectively.

From question:

             5x + 7y = 79                Eq. I

      and  7x + 5y = 77                 Eq. II

 

Adding Eq. I and Eq. II:

12x + 12y = 156

⇒ 12(x + y) = 156

⇒ x + y = 13         Eq. III

 

Subtracting Eq. I from Eq. II:

2x - 2y = - 2

⇒ x - y = - 1             Eq. IV

 

Adding Eq. III and Eq. IV:

2x = 12

⇒ x = 12/2 = 6

 

Substitute x = 6 in Eq. III:

6 + y = 13

⇒ y = 13 - 6 = 7

 

 

So, the cost of 1 book and 2 pens = 6 + 2 (7) =Rs. 20

The cost of 1 book and 2 pens is Rs. 20