Question

Jason and Sandra had a day off from work on October 1. Jason is off work every third day, and Sandra is off from work every fourth day. When is the next day both Jason and Sandra will be off work?

Answer 1

Jason and Sandra will next have the same day off on October 12th. This is found by calculating the Least Common Multiple (LCM) of their work cycles, which is 12 days.

Step-by-step explanation:

To find the next day that both Jason and Sandra will have off from work, we need to calculate the Least Common Multiple (LCM) of their work cycles. Since Jason is off every third day and Sandra is off every fourth day, we will find the LCM of 3 (Jason's cycle) and 4 (Sandra's cycle).

1. Identify the multiples of Jason's cycle: 3, 6, 9, 12, 15, ...
2. Identify the multiples of Sandra's cycle: 4, 8, 12, 16, 20, ...
3. Find the smallest multiple that is common to both lists: The LCM of 3 and 4 is 12.
4. Count 12 days from October 1st to find the next day they both have off. Since October 1st is included, we count: October 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. So, the next day they both have off is October 12th.