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A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Arushi paid Rs.27 for a book kept for seven days. If fixed charges are Rs.$x$ and per day charges are Rs.$y$. Write the linear equation representing the above information.

Last updated date: 21st Mar 2023
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Hint- Sum of fixed charges and additional charges of library is Rs.27

Given data:
Fixed charge is $x$Rs. for the first three days.
And after that per day charges are$y$Rs.
But Arushi kept the book for 7 days.
So, remaining day’s \[{\text{ = 7 - 3 = 4}}\]days.
$\therefore $ Additional charges $ = $($4 \times $(Price for per day charge))
It is given that Arushi paid Rs. 27 for the book
Now according to given condition
Fixed charges $ + $ additional charges $ = $Rs.27
$\therefore $Fixed charges$ + $ ($4 \times $(Price for per day charge))$ = 27$
\[ \Rightarrow x + 4y = 27\]
So, this is the required linear equation.

Note- Whenever we face such types of questions first find out the remaining days for which additional charges are applied , then according to the given condition which is written above formulate the linear equation, we will get the required linear equation representing the above information.