Question

A library has a fixed charge for the first 3 days and an additional charge each day thereafter. Arushi paid Rs. 27 for a book kept for 7 days in fixed charge of Rs. x and per day charges are Rs. y
Write the linear equation representing the above information.

Answer 1

Hint: We know that a linear equation is an equation of the form \[ax+b\], where a and b are constants. The given equation is called a linear equation because on a graph it represents a straight line. It is given in the question that Arushi has to pay Rs. x as fixed charge for first 3 days thereafter she has to pay Rs. y per day as additional charge for each day she has taken a book after 3 days. So we total total cost by adding fixed cost and additional cost incurred.

Complete step-by-step answer:
An equation can be defined as the statement which shows the equality of two expressions separated by equal sign or we can say, if a function is assigned a particular value then it is called an equation.
We are aware that a linear equation is an equation of the form \[ax+by+c=0\], where a and b are constants. We trace the graph of a linear function on a graph it appears as a straight line.
For the first 3 days she has to pay a fixed fee of Rs. x which needs to be paid even if she takes the book for one book.
\[{{S}_{f}}=x\], Where \[{{S}_{f}}\] is fixed price
For every day after 3 days, Arushi has to pay Rs. y so we add it to original fixed price,
\[{{S}_{N}}=7y\], Where \[{{S}_{N}}\] is per day income
Since total is Rs. 27 then \[{{S}_{N}}\]+ \[{{S}_{f}}\] is given as 27
\[x+7y=27\]
Hence the acquired result is :– \[x+7y=27\]

Note: The student must make sure that he knows what linear equation and how to form one by using elementary ideas presented in the questions. The common mistakes committed are wrong use of formula and incorrect general formula.