Question

18 Notebooks and 32 pens together cost Rs. 642, while 32 notebooks and 18 pencils together cost Rs. 908. Find the cost of each notebook.​

Answer 1

Given :

• 18 Notebooks and 32 pens together cost Rs. 642.
• 32 notebooks and 18 *pens* together cost Rs. 908.

To Find :

• Cost of each notebook
• Cost of each pens

Solution :

Let the cost of each notebooks be ₹ x.

Let the cost of each pen be ₹ y.

Case 1 :

Cost of 18 notebook and 32 pens is ₹ 642.

Equation :

$\longrightarrow$ $\sf{18x+32y=642}$

$\longrightarrow$ $\sf{18x=642-32y}$

$\sf{x=\dfrac{642-32y}{18}\:\:(i)}$

Case 2 :

Cost of 32 notebooks and 18 pens cost ₹ 908 altogether.

Equation :

$\sf{32x+18y=908}$

From equation (i),

$\longrightarrow$ $\sf{32\:\times\:\big(\dfrac{642-32y}{18}\big)\:+\:18y\:=\:908}$

$\longrightarrow$ $\sf{\dfrac{20544-1024y}{18}+18y=908}$

$\longrightarrow$ $\sf{\dfrac{20544\:-\:1024y+324y}{18}\:=\:908}$

$\longrightarrow$ $\sf{\dfrac{20544-700y}{18}=908}$

$\longrightarrow$ $\sf{20544-700y=908\:\times\:18}$

$\longrightarrow$ $\sf{20544-700y=16344}$

$\longrightarrow$ $\sf{-700y=16344-20544}$

$\longrightarrow$ $\sf{-700y=-4200}$

$\longrightarrow$ $\sf{y=\dfrac{\cancel{-}42\cancel{00}}{\cancel{-}7\cancel{00}}}$

$\longrightarrow$ $\sf{y=\cancel\dfrac{42}{7}}$

$\longrightarrow$ $\sf{y=6}$

Substitute, y = 6 in equation (i),

$\longrightarrow$ $\sf{x=\dfrac{642-32y}{18}}$

$\longrightarrow$ $\sf{x=\dfrac{642-32(6)}{18}}$

$\longrightarrow$ $\sf{x=\dfrac{642-192}{18}}$

$\longrightarrow$ $\sf{x=\cancel\dfrac{450}{18}}$

$\longrightarrow$$\sf{x=25}$

$\large{\boxed{\sf{\purple{Cost\:of\:each\:notebook\:=\:x\:=\:Rs.\:25}}}}$

$\large{\boxed{\sf{\purple{Cost\:of\:each\:pen\:=\:y\:=\:Rs.\:6}}}}$