Question

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
A part of monthly hotel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days, she has to pay Rs.1000 as hostel charges whereas a student B, who takes food 26 days, pays Rs.1180 as hostel charges. Find the fixed charges and the cost of food per day.

Answer 1

Hint: In this problem, we have to form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method. We can solve the given equations one by one by forming equations and simplifying it by eliminations if they exist.

Complete step by step solution:
Student A takes food for 20 days, she has to pay Rs.1000 as hostel charges whereas student B, who takes food 26 days, pays Rs.1180 as hostel charges. Find the fixed charges and the cost of food per day.
We can now form equations with the given data.
We can take x as the fixed charge and y as the charge of food per day
\[\begin{align}
  & x+20y=1000.......(1) \\
 & x+26y=1180.......(2) \\
\end{align}\]
We can subtract (1) and (2), we get
\[\begin{align}
  & \Rightarrow 6y=180 \\
 & \Rightarrow y=30 \\
\end{align}\]
We can substitute the y value in (1), we get
\[\begin{align}
  & \Rightarrow x=1180-26\times 30 \\
 & \Rightarrow x=400 \\
\end{align}\]
Therefore, the fixed charge is Rs.400 and charge per day is Rs.30.

Note: Students make mistakes while forming equations to be solved and to find the value unknown variable. We should concentrate while forming an equation, where the unknown variable is the data to be found and what is required. We can then substitute one value in one of the equations to get the other value as well.