Question

The cost of 2 books and 6 notebooks is Rs. 34 and the cost of 3 books and 4 notebooks is Rs. 31. Express the given problem in linear equations.

Answer 1

Hint: Assume the books as ‘x’ and the notebooks as ‘y’. Form the first linear equation by considering the statement ‘the cost of 2 books and 6 notebooks is Rs. 34’. Similarly form the second linear equation by considering the statement ‘the cost of 3 books and 4 notebooks is Rs. 31’.

Complete step-by-step solution:
Let the books be denoted as ‘x’ and the notebooks be denoted as ‘y’.
So, 2 books$=2\times x=2x$ and 6 notebooks$=6\times y=6y$
Hence, the cost of 2 books and 6 notebooks is Rs. 34 can be written as $2x+6y=34$
Again, 3 books$=3\times x=3x$ and 4 notebooks$=4\times y=4y$
Hence, the cost of 3 books and 4 notebooks is Rs. 31 can be written as $3x+4y=31$
So, the linear equations are
$2x+6y=34$
$3x+4y=31$
This is the required solution for the given question.

Note: The linear equations we obtained can be solved as simultaneous equations. The equations we have
$2x+6y=34$……….(1)
$3x+4y=31$……….(2)
To equate the ‘x’ coefficient of both the equations equation(1) should be multiplied by 3 and equation(2) should be multiplied by 2.
$eq(1)\times 3\Rightarrow 6x+18y=102$……….(3)
$eq(2)\times 2\Rightarrow 6x+8y=62$……….(4)
Subtracting equation (4) from equation (3), we get
$\begin{align}
  & \left( 6x+18y \right)-\left( 6x+8y \right)=102-62 \\
 & \Rightarrow 6x+18y-6x-8y=40 \\
 & \Rightarrow 10y=40 \\
 & \Rightarrow y=\dfrac{40}{10} \\
 & \Rightarrow y=4 \\
\end{align}$
Putting the value of ‘y’ in any of the above equation we can obtain the value of ‘x’.
Putting $y=4$ in equation (2), we get
$\begin{align}
  & 3x+4y=31 \\
 & \Rightarrow 3x+4\times 4=31 \\
 & \Rightarrow 3x+16=31 \\
 & \Rightarrow 3x=31-16 \\
 & \Rightarrow 3x=15 \\
 & \Rightarrow x=\dfrac{15}{3} \\
 & \Rightarrow x=5 \\
\end{align}$
So, the solution of the linear equations $2x+6y=34$ and $3x+4y=31$is $x=5$ and $y=4$.