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.