Total boarding expenses of a boarding house are partly fixed and partl

Solution:

We can set up the equation y = k + nx, where y is the total expenses when there are x boarders and k and n are some constants. Thus, we can create the equations:

1200 = k + 40n

1200 - 40n = k

and

1500 = k + 55n

Substituting, we have:

1500 = 1200 - 40n + 55n

300 = 15n

20 = n

Thus, k = 1200 - 40(20) 1200 - 800 = 400.

So, when there are 75 boarders, the cost is:

400 + 75(20) = 400 + 1500 = 1900

Alternate Solution:

Since the boarding expenses vary linearly with the number of boarders, we see that 55 - 40 = 15 boarders cost 1500 - 1200 = 300 dollars more in boarding expenses. That is, an extra boarder would cost 300/15 = 20 dollars more in boarding expenses. Since 75 - 55 = 20, 75 boarders would cost 20 x 20 = 400 dollars more in boarding expenses than 55 boarders. Therefore, the total expenses of 75 boarders is 1500 + 400 = 1900 dollars.


Answer: B

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