Question

The total cost of 8 books and 5 pens is $₹420$ and the total cost of 5 books and 8 pens is ₹321. Find the cost of 1 book and 2 pens.

Answer 1

Let the cost of one book be $₹x$ and the cost of one pen be $₹y$.
According to the first condition, the total cost of 8 books and 5 pens is ₹ 420 .
$$\therefore 8x+5y=420\text{...(i)}$$
According to the second condition, the total cost of 5 books and 8 pens is ₹ 321 .
$$5x+8y=321\text{....(ii)}$$
Multiplying equation (i) by 5 ,
$$40x+25y=2100\text{...(iii)}$$
Multiplying equation (ii) by 8 ,
$$40x+64y=2568\dots \text{(iv)}$$
Subtracting equation (iii) from (iv),
$\begin{array}{cc}& 40x+64y=2568\\ 40x+25y& =2100\\ ---& \\ 39y& =468\\ \therefore y=\frac{468}{39}& \\ \therefore y=& 12\end{array}$
Substituting $y=12$ in equation (i),
$$\begin{array}{cc}& 8x+5y=420\\ & \therefore 8x+5\left(12\right)=420\\ & \therefore 8x+60=420\\ & \therefore 8x=420-60\\ & \therefore 8x=360\\ & \therefore x=\frac{360}{8}\\ & \therefore x=45\end{array}$$
Cost of 1 book and 2 pens $=x+2y$
$$\begin{array}{cc}& =45+2\left(12\right)\\ & =45+24\\ & =₹69\end{array}$$
$\therefore$ The cost of 1 book and 2 pens is ₹ 69 .