Final answer:
To find the number of students who didn't participate, subtract the number of students who did participate from the total number of students at Maryville High School. One-fifth of the students signed a pledge and a third of the students promised to talk to someone who smoked.
Step-by-step explanation:
To find the number of students who didn't participate in the Great American Smokeout, we need to subtract the number of students who did participate from the total number of students at Maryville High School.
One-fifth of the students signed a pledge, which is equal to 1/5 * 1066 = 213 students.
A third of the students promised to talk to someone who smoked, which is equal to 1/3 * 1066 = 355.33 students. Since we can't have a fractional number of students, we round down to 355 students.
To find the number of students who didn't participate, we subtract the students who signed a pledge and the students who promised to talk to someone from the total number of students: 1066 - 213 - 355 = 498 students.