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

Question

1
4
the total number of students, while Group B has 3 less than the total number of students. Which inequality represents this situation?

Responses

1
4
t
+
6
<
t
−
3
1 4 t + 6 < t − 3

(
1
4
+
6
)
t
<
t
−
3
( 1 4 + 6 ) t < t − 3

1
4
t
+
6
<
3
−
t
1 4 t + 6 < 3 − t

6
t
+
1
4
<
t
−
3

Answer 1

To form the inequalities correctly based on the situation described, let's break it down step-by-step:

1. Group A's Students: The number of students in Group A is stated to be "6 more than \( \frac{1}{4} \) of the total number of students."

   • This can be represented as: \[ A = \frac{1}{4}t + 6 \]

2. Group B's Students: The number of students in Group B is stated to be "3 less than the total number of students."

   • This can be expressed as: \[ B = t - 3 \]

3. Inequality Between Groups: It is given that the number of students in Group A is less than the number of students in Group B, which gives us the inequality: \[ A < B \]

Using the expressions for A and B we established earlier, we can substitute into the inequality: \[ \frac{1}{4}t + 6 < t - 3 \]

This inequality accurately represents the situation described. Therefore, the correct response is:

\[ \frac{1}{4} t + 6 < t - 3 \]