PSAT Math Grid-Ins Question 134: Answer and Explanation

Question: 134

The scatter plot above shows the price of a room per night at 15 different hotels versus the distance the hotels are from the beach. If Hotel M is the hotel at the median distance to the beach, how many hotel rooms must be booked for the hotel to make $2,280 in one night?

Correct Answer: 19

Explanation:

(19) The hotel at the median distance in a series of 15 terms will have 7 terms on both sides. Therefore, the hotel that we are looking for is the 8th term. Count 8 points from the left. Then follow that point along to the y-axis to find its cost per night. The cost per night at Hotel M is $120.

Let x be the number of rooms the hotel books. Since the hotel wants to make $2,280 and each room costs $120, we have the following equation: 2,280 = 120x. Divide $2,280 by $120 to tell how many rooms must be booked:

$2,280 ÷ $120 = 19

So 19 rooms must be booked. Alternatively, we could have used dimensional analysis in the last step to eliminate units that we didn't want: