Krista G. answered • 11/15/19
Professional Editor, Writer - English + Sociology
Alright, let's start with thinking about this without a formula. Pizza is every fourth day. Let's write this out with a small sample. X will mark days that pizza is served.
1 2 3 X 5 6 7 X 9 10 11 X 13 14 15 X 17 18 19 X
In other words, every four days, pizza is served.
Now let's look at tacos. Tacos are served every third day. Let's start from 1 again, and have Y mark tacos days.
1 2 Y 4 5 Y 7 8 Y 10 11 Y 13 14 Y 16 17 Y 19 20
Do you see any times X and Y happen on the same number? Yes! We see this only on one day: the 12th day. So we can think of this as where every 3rd and every 4th day meet. If we want to get into the advanced math of this, we would see that the only factor they share is 1, meaning the soonest every 3rd and every 4th event meets would be every 12th event.
In other words, every 12 days, both pizza and tacos are served.
The end of your question seems to be asking how many more times both will occur in the year. You'd find this by finding out how many days are left in the school year and dividing by 12, then rounding down to the lowest whole number. Let's say there were 100 days left. 100 / 12 = 8.33. Since we can't divide days into fractions where you get 1/3 tacos and 1/3 pizzas or something crazy like that, we round this down to 8. So there would be 8 days left in the year where both are served, and the final few days of the semester wouldn't have them both.
I hope that helped!
