Question

A theater gives away one free ticket to every 10th customer and two free tickets to every 25th customer. The manager wants to give away four free tickets when the customer is both a 10th and a 25th customer. Who is the first customer that will recieve four free tickets

Answer 1

The first customer that will get four free tickets is 50th customer

Explanation:

Find the least common multiple of numbers 10 and 25. First, factorize these numbers:

`10=2\cdot \underline{5}\\ \\25=\underline{5}\cdot 5\\ \\LCM(10,25)=\underline{5}\cdot 2\cdot 5=50`

When finding LCM, first write the all common multiples (underlined 5) and then multiply them by remaining multiples (2 and 5). You get 50 as LCM(10,25). This means that each 50th customer will get four free tickets.