Bunuel wrote:
Total boarding expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The total boarding expenses is $1200 when there are 40 boarders and is $1500 when there are 55 boarders. What is the total boarding expenses when there are 75 boarders?
A. $1800
B. $1900
C. $2000
D. $2100
E. $2200
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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