The manager has given away a total of 24 free tickets.
Let's break down the information:
Every 10th customer gets one free ticket.
Every 25th customer gets two free tickets.
The manager wants to give away four free tickets when a customer is both the 10th and 25th customer.
Now, we can calculate the number of customers who are both the 10th and 25th:
Customers who get 1 free ticket:
120/10 =12
Customers who get 2 free tickets:
120/25 =4
However, we have counted the ones who get both (10th and 25th) twice, so we need to subtract that:
Customers who get both 1 and 2 free tickets:
120/10×25 =1
Now, let's calculate the total number of free tickets given away:
Free tickets for 10th customers:
Free tickets for 10th customers: 12×1=12
Free tickets for 25th customers:
Free tickets for 25th customers: 4×2=8
Free tickets for customers who are both 10th and 25th:
Free tickets for customers who are both 10th and 25th: 1×4=4
Adding them up:
12+8+4=24
So, the manager has given away a total of 24 free tickets.
Question
A theater gives away one free ticket to every 10 th 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 25th customer. If 120 customers have bought tickets today, how many free tickets has the manager given away?