The total number of students who could attend a field trip is represented by the variable t. The number of students in Group A is less than the number in Group B. Group A has 6 students more than 1 4 the total number of students, while Group B has 3 less than the total number of students. Which inequality represents this situation?

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,

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step-by-step explanation: