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To solve this problem, let’s break down the details provided and determine the correct inequalities:

1. **Objective**: Collect at least 100 cans but no more than 160 cans.
2. **Class Details**: There are 15 students in the class.
3. **Teacher’s Contribution**: The teacher has already pledged to bring in 10 cans.

Let \( n \) represent the number of cans each student should bring.

### Steps to Formulate the Inequality

1. **Total Cans Needed**: The total cans collected must be between 100 and 160.
2. **Contribution by Students and Teacher**:
   - The 15 students each bring \( n \) cans, contributing a total of \( 15n \) cans.
   - The teacher adds 10 cans to this, so the total number of cans is \( 15n + 10 \).

3. **Setting up the Inequality**:
   - We want \( 15n + 10 \) to be at least 100 and at most 160. Therefore, the inequality becomes:
     \[
     100 \leq 15n + 10 \leq 160
     \]

### Answer

The correct inequality that represents the possible numbers of cans \( n \) that each student should bring is:
\[
100 \leq 15n + 10 \leq 160
\]

So, the answer is the option:
- \( 100 \leq 15n + 10 \leq 160 \)

Would you like further details on how to solve this inequality step-by-step?

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Here are some related questions for further practice:

1. How would the inequality change if the teacher brought in 15 cans instead of 10?
2. What if the goal was to collect exactly 150 cans, rather than a range?
3. How would the inequality change if there were only 10 students in the class?
4. What if each student could only bring a maximum of 8 cans?
5. How many cans would each student need to bring if the teacher did not contribute any cans?

**Tip**: When setting up inequalities, always carefully account for contributions from all sources and any specified range or limit conditions.

Your math class is collecting canned food for a local food drive. The goal is to collect at least 100 cans but no more than 160 cans due to space limitations. There are 15 students in your math class and your teacher has promised to bring in 10 cans. Select which inequalities represent the possible numbers n of cans that each student should bring in.

Solve an inequality problem involving a food drive collection goal. With 15 students and a teacher’s contribution, determine the range of cans each student should bring to meet a goal between 100 and 160 cans. Ideal for Grades 7-8 students learning algebraic inequalities.

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