Final answer:
The ratio of teachers to students is 1:4, and the question asks for the number of teachers on a field trip with 36 people in total. By dividing the total number of people by the size of the ratio group (5), we find there are 7 groups, which leads to the conclusion that there are 7 teachers on the trip.
Step-by-step explanation:
The question requires solving a ratio problem to determine the number of teachers on a field trip based on the given ratio of teachers to students and the total number of people on the trip. Since the ratio of teachers to students is 1 to 4, we can use this ratio to set up a proportion to find out how many teachers there are out of the total 36 people.
Let's denote the number of teachers as T and the number of students as S. The ratio of teachers to students is written as T:S = 1:4. This means for every teacher, there are 4 students. If we add both parts of the ratio together, 1 for the teacher and 4 for the students, we get a group of 5. To find out how many groups of 5 there are in 36 (the total number of people), we divide 36 by 5, which equals 7.2. Since we cannot have a fractional part of a teacher or student, this means there are 7 groups exactly, and 1 person is not included in the ratio.
Now, we multiply the number of groups by the number of teachers per group (which is 1, from the ratio). So we have 7 groups × 1 teacher/group = 7 teachers.
Therefore, the correct option for the number of teachers on the field trip is 7.