A hotel finds that if it spends no money on renovations, they will be able to rent 135 rooms per night. However, they have found that for every $4000 spent on renovations, they will be able to rent an additional 30 rooms per night. Let x represent the amount of money spent on renovations and y represent the number of rooms rented. Determine a model for the number of rooms rented as a function of the amount of money spent on renovations.
A) y = 135 + 30 x
B) y = 135 + x
C) y = 135 + x
D) y = 135 + x
E) y = 135 + 4000 x

Question

A hotel finds that if it spends no money on renovations, they will be able to rent 135 rooms per night. However, they have found that for every $4000 spent on renovations, they will be able to rent an additional 30 rooms per night. Let x represent the amount of money spent on renovations and y represent the number of rooms rented. Determine a model for the number of rooms rented as a function of the amount of money spent on renovations.
A) y = 135 + 30 x 
B) y = 135 + x 
C) y = 135 + x 
D) y = 135 + x 
E) y = 135 + 4000 x

Quizplus · Accepted Answer

We know that if the hotel spends no money on renovations, they will be able to rent 135 rooms per night. This gives us the y-intercept of the function, which is 135. We also know that for every $4000 spent on renovations, the hotel can rent an additional 30 rooms per night. This gives us the slope of the function, which is 30/4000 or 0.0075. Thus, the model for the number of rooms rented as a function of the amount of money spent on renovations is: y = 135 + 0.0075x. However, in answer choice C, the coefficients have been multiplied by 1000 to eliminate the decimal: y = 135 + 11.25x. This is equivalent to y = 135 + 11ec1b6e_3c47_4998_bbf8_9fa788f4337e_TBX8728_11 x. Therefore, answer choice C is the best choice.

A Hotel Finds That If It Spends No Money on Renovations