Question

At the movie theatre, they give out a free drink to every 5th customer and a free bag of popcorn to every 9th customer. What was the first customer to get both a free drink and free popcorn? If 100 people came to the theater, how many people received both free items?

A) The first customer to get both was the 45th customer.
B) The first customer to get both was the 9th customer.
C) The first customer to get both was the 5th customer.
D) The first customer to get both was the 40th customer.

Answer 1

The first customer to receive both a free drink and free popcorn was the 45th customer. If 100 people came to the theater, only one person received both free items.

Step-by-step explanation:

To determine the first customer who received both a free drink and free popcorn, we need to find the least common multiple (LCM) of 5 and 9. The LCM of 5 and 9 is the smallest number that is divisible by both 5 and 9.

• Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
• Multiples of 9: 9, 18, 27, 36, 45, 54, ...

The first number that appears in both lists is 45, which means the 45th customer is the first to receive both a free drink and free popcorn.

Now, if 100 people came to the theater, the number of people who received both items is the count of multiples of 45 that are less than or equal to 100. There is only one such number, which is 45 itself, so only one person received both free items.