Question

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?

Answer 1

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