Artie and Billy shop at the same grocery store between 5 and 6 in
the evening.The last time they saw each other was on Tuesday.Artie shops every 5 days and Billy shops every 4 days.What day of the week will they next run into each other at the store,assuming that the store is open 7 days a week?
saturday
6weeks later.
To determine the next day they will run into each other at the store, we need to find the least common multiple (LCM) of 5 and 4.
To find the LCM, we can list the multiples of each number until we find a common multiple.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
From the lists, we can see that 20 is the least common multiple of 5 and 4.
Since Artie shops every 5 days and Billy shops every 4 days, they will both shop on the same day every 20 days.
Given that the last time they saw each other was on Tuesday, we can count 20 days from that day to determine the next day they will meet.
Starting from Tuesday:
Tuesday (day 1)
Wednesday (day 2)
Thursday (day 3)
Friday (day 4)
Saturday (day 5)
Sunday (day 6)
Monday (day 7)
Tuesday (day 8)
Wednesday (day 9)
Thursday (day 10)
Friday (day 11)
Saturday (day 12)
Sunday (day 13)
Monday (day 14)
Tuesday (day 15)
Wednesday (day 16)
Thursday (day 17)
Friday (day 18)
Saturday (day 19)
Sunday (day 20)
Therefore, they will next run into each other on Sunday.
So, the day of the week they will next run into each other at the store is Sunday.