Question

a part of a monthly hostel charges is fixed and the remaining depends on the number of the days one has taken food in the Mars when the student takes food for 20 days he has 1000 rupees has a hotel charges where as a student be who takes a food for 26 day pays 1180 as a hotel charges find the fixed charge and the cost of the per day in substitution method​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

• A part of a monthly hostel charges is fixed and the remaining depends on the number of the days one has taken food in the mess.

Let assume that

• A part of monthly hostel charges = Rs x

• Cost per day of food in mess = Rs y

According to first condition

When the student takes food for 20 days, he has Rs 1000 has a hostel charges.

So,

$\rm :\longmapsto\:x + 20y = 1000$

$\rm \implies\: \boxed{ \rm \: x = 1000 - 20y \: } - - - (1)$

According to second condition

A student be who takes a food for 26 day pays Rs 1180 as a hostel charges.

$\rm :\longmapsto\:x + 26y = 1180$

$\rm :\longmapsto\:1000 - 20y + 26y = 1180$

$\rm :\longmapsto\:1000 + 6y = 1180$

$\rm :\longmapsto\: 6y = 1180 - 1000$

$\rm :\longmapsto\: 6y = 180$

$\rm \implies\: \boxed{ \rm \: y = 30 \: }$

On substituting y = 30, in equation (1), we get

$\rm :\longmapsto\:x = 1000 - 30 \times 20$

$\rm :\longmapsto\:x = 1000 - 600$

$\rm \implies\: \boxed{ \rm \: x = 400 \: }$

So,

A part of monthly hostel charges = Rs 400

Cost per day of food in mess = Rs 30

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Additional Information :-

There are 4 methods to solve this type of pair of linear equations.

1. Method of Substitution

2. Method of Eliminations

3. Method of Cross Multiplication

4. Graphical Method

Method of Substitution

To solve systems using substitution, follow this procedure:

Select one equation and solve it to get one variable in terms of second variables.

In the second equation, substitute the value of variable evaluated in Step 1 to reduce the equation to one variable.

Solve the new equation to get the value of one variable.

Substitute the value found in to any one of two equations involving both variables and solve for the other variable.