Question

The total cost of 6 books and 7 pens is 79 rupees and the total cost of 7 books and 5 pens is 77 rupeess. Find the cost of 1 book and 2 pens.

Answer 1

Disclaimer: There is an error in the given question. Instead of 7 books and 5 pens there should be 7 books and 6 pens.

Let the cost of 1 book be x and the cost of 1 pen be y.
The total cost of 6 books and 7 pens is 79 rupees.
$6x+7y=79.....\left(\mathrm{I}\right)$
Total cost of 7 books and 6 pens is 77 rupeess.
$7x+6y=77.....\left(\mathrm{II}\right)$
Adding (I) and (II)
$$\begin{gathered} 13x+13y=156 \\ \Rightarrow x+y=12.....\left(\mathrm{III}\right) \end{gathered}$$
Subtracting (II) from (I)
$x-y=-2.....\left(\mathrm{IV}\right)$
Adding (III) and (IV)
$$\begin{gathered} 2x=10 \\ \Rightarrow x=5 \end{gathered}$$
y = 7
Cost of 1 book and 2 pens is 5 + 14 = Rs 19.