Question

the expenses of a boarding house is partly fixed and partly varies with the number of boarders. Each boarder pays $390 a month. The profits are $54 per head per month. When there are 60 boarders, what is the profit per head per month where there are 80 boarders​

Answer 1

The profit per head per month when there are 80 boarders is $162.

Step-by-step explanation:

Let's first determine the fixed cost of the boarding house. We know that the profit per head per month is $54 and each boarder pays $390 a month. So, the variable cost per head per month is $390 - $54 = $336. Let's assume the fixed cost is F.

When there are 60 boarders, the total cost is 60 x $336 = $20,160.

Now, let's determine the fixed cost using the given information. We know that the profit per head per month is $54 and each boarder pays $390 a month. So, the variable cost per head per month is $390 - $54 = $336. At this point, the total cost is $20,160. Now, assuming the total cost remains the same when there are 80 boarders, we can calculate the profit per head per month by dividing the remaining cost by the number of boarders, which gives us ($20,160 - $F) / 80 = $54. Solving this equation, we find that the fixed cost is $6,240.

Therefore, when there are 80 boarders, the profit per head per month where there are 80 boarders is ($20,160 - $6,240) / 80 = $162.