Question

3 pens, 4 notebooks together cost Rs. 110, and 7 pens, 5 notebooks cost Rs. 170. Find the cost of each pen and notebook.

Answer 1

Hint: For solving this question first we will assume the cost of 1 pen and 1 notebook in terms of variables. Then, we will form equations in terms of variables and then solve these equations to get the correct answer.

Complete step-by-step solution -
Given:
Cost of 3 pens and 4 notebooks together is Rs. 110. And the cost of 7 pens and 5 notebooks is Rs. 170.
Now, let the cost of one pen is Rs. $x$ and the cost of one notebook is Rs. $y$ . Then,
Cost of 3 pens and 4 notebooks together in Rs. $=3x+4y$ .
It is given that the cost of 3 pens and 4 notebooks together is Rs. 110. Then,
$3x+4y=110..........\left( 1 \right)$
Cost of 7 pens and 5 notebooks together in Rs. $=7x+5y$ .
It is given that the cost of 7 pens and 5 notebooks together is Rs. 170. Then,
$7x+5y=170...........\left( 2 \right)$
Now, multiply (1) by 5 and multiply (2) by 4 and subtract them. Then,
$\begin{align}
  & 5\times \left( 3x+4y \right)-4\times \left( 7x+5y \right)=5\times 110-4\times 170 \\
 & \Rightarrow 15x-28x=550-680 \\
 & \Rightarrow -13x=-130 \\
 & \Rightarrow x=10 \\
\end{align}$
Now, put $x=10$ from above equation in equation (1). Then,
$\begin{align}
  & 3x+4y=110 \\
 & \Rightarrow 30+4y=110 \\
 & \Rightarrow 4y=80 \\
 & \Rightarrow y=20 \\
\end{align}$
Thus, from the above calculations, we can say that the value of $x=10$ and $y=20$ .
Hence, the cost of a pen is Rs. 10 per piece and the cost of the notebook is Rs. 20 per piece.

Note: Although the question was very easy to solve but here the student should frame the equations correctly as per the given data and then solve the equations without any calculation mistake to get the correct answer.Here we can also Use the addition method to solve the linear equation, where we first form the equations in such a way that one variable has alternate sign .