Question

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is $	ext{Rs. } 700$ when there are $25$ boarders and $	ext{Rs. } 600$ when there are $50$ boarders. What is the average expense per boarder when there are $100$ boarders?

Accepted Answer

A. Let total expense $E = F + nV$. For $n = 25$: $25 	imes 700 = 17500 = F + 25V$. For $n = 50$: $50 	imes 600 = 30000 = F + 50V$. Subtracting: $25V = 12500 \implies V = 500$. Then $F = 17500 - 25(500) = 5000$. For $n = 100$: Total expense = $5000 + 100(500) = 55000$. Average expense per boarder = $\frac{55000}{100} = 550$.

Linear Function: Boarding House Expenses

Explanation

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