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A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess
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 student A takes food for 20 days, she has to pay Rs 1000 as hostel charges whereas 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.
Expert Solution
The number of days a student eats in the mess can be given by x. Let the fixed cost be A and the variable cost be Y. The monthly charges can be given by [Math Processing Error]C=A+Bx
When, x=20, C=$1000 thus:
[Math Processing Error]1000=A+20B
When x=26, C=$1180 thus:
[Math Processing Error]1180=A+26B
Subtracting the two equations:
[Math Processing Error]1180−1000=A−A+26B−20B180=6BB=1806=30
To find A:
[Math Processing Error]1000=A+20×301000=A+600A=400
Hence, the fixed charges are $400 and the cost of food per day are $30.
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