SAT Math Multiple Choice Practice Question 578: Answer and Explanation

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Question: 578

14. The total cost to hold a party at a banquet hall is the result when the product of the number of guests and the cost of food per person is added to the product of the hourly cost to rent the hall and the number of hours the party will last. One hundred guests have been invited, the food costs a total of $200, and the hall charges $50 per hour. To save money, the organizers would like to reduce the length of the party from 4 hours to 2 hours. How much money would the organizers save by reducing the length of the party?

A. $400
B. $300
C. $200
D. $100
E. The price will not change.

Correct Answer: D


D Use Bite-Sized Pieces with a wordy question like this. To paraphrase, the question states that total cost = (food cost × number of people) + (hourly cost × number of hours). We are given the total cost of the food, so we don't need to use the number of people we are given. We are also told the hourly cost in the question, but need to find the difference in cost for a two-hour and a four-hour party: 200 + (50 × 2) = 300 and 200 + (50 × 4) = 400, so there is a difference in cost of $100.

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