Question

Form the pair of linear equations in the following problem and find their solution (if they exist) by any algebraic method:

A part of monthly hostel 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 for $26$ days, pays $Rs.1180$ as hostel charges. Find the fixed charges and the cost of food per day.

Answer 1

Step 1: Form the linear equations

Let us assume that

The fixed charge is $x$.

The charge of food per day is $y$.

According to the given data

$x+20y=1000\dots \dots \dots \dots \left(i\right)$

$x+26y=1180\dots \dots \dots \dots \left(ii\right)$

Step 2: Find the solution

On subtracting $\left(i\right)$ from $\left(ii\right)$ we get

$x+20y-x-26y=1000-1180$

$\Rightarrow$ $26y–20y=180$

$\Rightarrow$ $6y=180$

$\Rightarrow$ $y=Rs.30$

Substituting $y=30$ in equation $\left(ii\right)$ we get

$x=1180-(26x30)$

$=Rs.400$

Hence, fixed charges are $Rs.400$ and the charge per day is $Rs.30$.