This is the information about students participating in a field trip:

36 were female students, 13 were male seniors, 41 were not drama majors, exactly half of the drama majors were male, a third of the female students were drama majors but not seniors, there were 15 senior drama majors 20% of which were male. How many students were on the trip?

Answer choices: A.89 B.99 C.105 D.None of them

To find the number of students on the field trip, let's break down the given information step-by-step:

Let's assign variables to the unknown quantities:
Let F represent the number of female students.
Let M represent the number of male students.
Let S represent the number of senior students.
Let D represent the number of drama majors.

1. We are given that 36 were female students, so F = 36.

2. 13 were male seniors, so S + M = 13.

3. 41 were not drama majors, so the total number of students who were drama majors is F + M + D = Total - 41.

4. Exactly half of the drama majors were male, so M = D/2.

5. A third of the female students were drama majors but not seniors, so (1/3)F = D - S.

6. There were 15 senior drama majors, so S = 15.

7. 20% of the senior drama majors were male, so M = (20/100) * 15.

Let's use this information to solve for the unknowns and find the total number of students (F + M):

From equation 2: S + M = 13
Substituting equation 6: 15 + M = 13
Solving for M: M = 13 - 15 = -2

Since M cannot be negative, we can conclude that there was an error in the given information or question. Therefore, the correct answer is D. None of them.

To solve this problem, let's break down the information given:

1. 36 were female students.
2. 13 were male seniors.
3. 41 were not drama majors.
4. Exactly half of the drama majors were male.
5. A third of the female students were drama majors but not seniors.
6. There were 15 senior drama majors, 20% of which were male.

Let's assign variables to some of the unknowns:
Let's call the total number of students on the trip "T."
Let's call the number of female drama majors but not seniors "FDMNS."
Let's call the number of male drama majors but not seniors "MDMNS."
Let's call the number of female senior drama majors "FSDM."
Let's call the number of male senior drama majors "MSDM."
Now, let's analyze each piece of information to form equations.

From information 1, "36 were female students," we know that:
Female students = 36

From information 2, "13 were male seniors," we know that:
Male seniors = 13

From information 3, "41 were not drama majors," we know that:
Non-drama majors = 41

From information 4, "Exactly half of the drama majors were male," we can deduce:
Male drama majors = (Total drama majors) / 2

From information 5, "A third of the female students were drama majors but not seniors," we can deduce:
FDMNS = (1/3) × Female students

From information 6, "There were 15 senior drama majors, 20% of which were male," we can deduce:
MSDM = (20/100) × Senior drama majors
= (20/100) × 15

Now, let's calculate the values for each variable:

From information 1, Female students = 36

From information 2, Male seniors = 13

From information 3, Non-drama majors = 41

From information 4, Male drama majors = (Total drama majors) / 2

From information 5, FDMNS = (1/3) × Female students

From information 6, MSDM = (20/100) × 15

To find the number of students on the trip, we need to sum up the number of students in each category:

Total students = Female students + Male seniors + Non-drama majors + Drama majors
= 36 + 13 + 41 + (Male drama majors + Female drama majors + FDMNS + MSDM)

To simplify this equation, we need to express Male drama majors and Female drama majors in terms of known quantities:

Male drama majors = (Total drama majors) / 2
= (Male drama majors + Female drama majors + FDMNS + MSDM) / 2

Rearranging this equation, we get:
Male drama majors - Male drama majors / 2 = Female drama majors + FDMNS + MSDM / 2

Combining the terms, we have:
Male drama majors / 2 = Female drama majors + FDMNS + MSDM / 2

Substituting the previously calculated values, we have:
(Male drama majors) / 2 = (36/3) + (20/100) × 15 / 2

Now we can solve for Male drama majors:
Male drama majors = (36/3) + (20/100) × 15 / 2 × 2

After calculating this value, we can substitute it back into the equation for Total students and solve for T:

Total students = 36 + 13 + 41 + (Male drama majors + Female drama majors + FDMNS + MSDM)

Now you can substitute the calculated values into the equation to find the total number of students on the trip.