Question

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs \[27\] for a book kept for seven days, while Susy paid Rs \[21\] for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Answer 1

Hint- Use elimination method to solve the equation i.e. Make the coefficients equal to any of the one variable of the two equations and then subtract the equations.
According to the question
Let the fixed charge for first $3$ day \[ = x\] and additional charge per day \[ = y\]
As per the statement in the question it is given that saritha kept a book for $7$ days that means kept $4$ days additional.
Therefore, \[ \Rightarrow x + 4y = 27\] …………….(1)
Similarly, it is given that susy kept the book for $5$ days that means kept $2$ days additional.
Therefore, \[ \Rightarrow x + 2y = 21\] ……………..(2)
By subtracting eq(2) from eq(1), we get
\[
   \Rightarrow {\text{ }}\left( {x + 4y = 27} \right) \\
   \Rightarrow - \left( {x + 2y = 21} \right) \\
\]
Gives
\[ \Rightarrow 2y = 6 \Rightarrow y = 3\]
Now put the $y$ value in eq(1), we get
\[
   \Rightarrow x + 4 \times 3 = 27 \\
   \Rightarrow x = 15 \\
\]
So, the fixed charges are Rs.$15$ and
The additional charges for each extra day are Rs.$3$.
Note – Whenever this type of question appears read the question carefully, and note down given details and thereafter make the equations accordingly. Use the Elimination method to solve the two-equation made. The idea here is to solve one of the equations for one of the variables, and substitute the obtained variable value into any of the equations to get the other variable.