Answer:
Let's define:
A = # of students in group A
B = # of students in group B
C = # of students in group C.
"The total number of students who could attend a field trip is represented by the variable t."
This can be written as:
A + B + C = t.
"The number of students in Group A is less than the number in Group B."
Here we have a strictly "less than", then this is written as:
A < B.
"Group A has 6 students more than 1/4 the total number of students"
A = t/4 + 6
"Group B has 3 less than the total number of students"
B = t - 3.
Then we have the equations:
A + B + C = t.
A = t/4 + 6
B = t - 3.
A < B.
We could replace the second and third equatio in the fourth one, to get:
t/4 + 6 < t - 3.
t/4 + 9 < t
9 < t - t/4
9 < t*(4/4 - 1/4)
9 < t*(3/4)
(4/3)*9 < t
12 < t.
Then we found an inequality that defines the minimum possible value of t,
