How many days will one person be in the classroom?

Question

There are 252 days in the classroom which must be taught. One person can teach 12 classroom days in a row then must take 8 classroom days off. How many days will one person be in the classroom?

Answer 1

Rachel,

First notice that you have a repeating cycle of 20 days (primary teacher in first 12, then substitute in 8).

The number of cycles n = 252/20 = 12.6, so you have 12 complete cycles and a final 13th partial cycle of 12 days (=0.6 of 20) which happens to be taught by the primary teacher again. There is no need for a substitute in this 13th cycle.

 

Then let x= total # of days taught be the primary teacher

So x = 12*(n+1) = 12 * 13 = 156 days,   and the subs teach 8*12 or 96 days

CHECK: 156 + 96 = 252 days!