Question

(1) 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 * 1000 as hostel charges whereas a student B, who takes food for 26 days, pays 1180 as hostel charges. Find the fixed charges and the cost of food per day. Substitution method
​

Answer 1

Step-by-step explanation:

Let the fixed charge be y and the cost of food per day be x

Now,

Student A takes food for 20 days & pays 1000

20x + y = 1000 _(1)

Student B takes food for 26 days & pays 1180

26x + y = 1180 _(2)

Subtracting (1) & (2), we get,

6x = 180

x = 30

Putting x = 30 in (1), we get,

20(30) + y = 1000

600 + y = 1000

y = 400

Hence, the fixed charges are Rs. 400 and the cost of food per day is Rs. 30.

Answer 2

Given :-

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 * 1000 as hostel charges whereas a student B, who takes food for 26 days, pays 1180 as hostel charges

To Find :-

Find the fixed charges and the cost of food per day

Solution :-

Let us assume that the fixed charge is Rs. x and cost of food per day is Rs. y

20 × x + y = 1000

20x + y = 1000 (1)

In Case 2

26 × x + y = 1180

26x + y = 1180 (2)

Subtract both

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

26x - 20x = 180

6x = 180

x = 180/6

x = 30

Now Using 2

26(30) + y = 1180

780 + y = 1180

y = 1180 - 780

y = 400