Artie Choke and Tom A. Toe both shop at the same local grocery store between five and six in the evening. The last time they saw each other was on Tuesday. Artie shops every five days and Tom shops every four days. What day of the week will they next run into each other at the store, assuming that the store is open seven days a week?
I would start making a chart,
for Artie, his next shopping days are
5, 10, 15, 20, 25, 30,. . . days after Tuesday
for Tom, his next shopping days are
4, 8, 12, 16, 20, 24,
The first time they meet is the GCF of 4, and 5, or 20 days after Tuesday.
The day of the week is Tuesday + 20mod7, or Tuesday + 6 days, or a Monday
To find out when Artie Choke and Tom A. Toe will next run into each other at the store, we need to find the least common multiple (LCM) of the number of days it takes for each of them to shop.
Artie shops every 5 days, and Tom shops every 4 days. The LCM of 5 and 4 is 20.
This means that Artie and Tom will next run into each other after 20 days.
Since they last saw each other on a Tuesday, the next time they will see each other will be 20 days later on a Tuesday again.
Therefore, they will next run into each other at the store on a Tuesday.
To determine the next day of the week when Artie Choke and Tom A. Toe will run into each other at the store, we need to find the least common multiple (LCM) of their shopping intervals.
Artie Choke shops every 5 days.
Tom A. Toe shops every 4 days.
The LCM of 5 and 4 is 20.
This means that Artie Choke and Tom A. Toe will run into each other again after 20 days (or 20 shopping intervals).
To determine the day of the week, we can use the fact that there are 7 days in a week. The remainder when dividing 20 by 7 will give us the day of the week they will meet.
20 รท 7 = 2 remainder 6
Since the remainder is 6, they will meet on the 6th day of the week counting from the last time they saw each other.
Assuming they last saw each other on a Tuesday, counting forward 6 days, we find that they will next run into each other on a **Monday**.