Question

A group of people is waiting in line for a theater premiere. Every 6th person in line will receive a free theater ticket, and every 15th person will receive a gift card for $40. Which person is the first to win both prizes? If there are 200 people in line, how many people will receive both prizes?

A) The first person in line will win both prizes.
B) The 6th person in line will win both prizes.
C) The 15th person in line will win both prizes.
D) No one will win both prizes.

Answer 1

The first person in line who will win both a free theater ticket and a $40 gift card is the 30th person, and among 200 people in line, there will be 6 people who will receive both prizes.

Step-by-step explanation:

To determine which person is the first to win both a free theater ticket and a $40 gift card, we need to find the least common multiple (LCM) of 6 and 15. The LCM of two numbers is the smallest number that is a multiple of both numbers. In this case, the LCM of 6 and 15 is 30. Therefore, the first person in line that will receive both prizes is the 30th person.

Regarding how many people will receive both prizes if there are 200 people in line, we divide 200 by 30 (the LCM of 6 and 15) to find out how many people will fit this criteria within the group of 200. As a result, 6 people in line will receive both prizes since 200 divided by 30 equals approximately 6 with some remainder.