A mathe teacher decides to create several practice tests for her students before they take the SAT. She wants to make some non-calculator tests and some calculator tests os that her students will be able to practice both.She figures that each non-calculator test take her 3 hours to create, and each calculator test will take 4 hours to create. If she is willings to devote at most 6 hours per week of her time for the next 5 weeks to create the practice tests, and she wants to provide at least 8 practice tests, which of the following systems of inequalities can help her determine how many of each type of test she can create?

Options

A. `n+cge8`
`3n+4cle6`
B. `n+cge8`
`3n+4cle30`
C. `n+cle8`
`3n+4cge30`
D. `n+cge6`
`3n+4cle8`

Explanation

To solve the problem, we need to set up a system of inequalities based on the information provided. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( N \) = number of non-calculator tests
- \( C \) = number of calculator tests

### Step 2: Determine Time Constraints
The teacher is willing to devote at most 6 hours per week for 5 weeks. Therefore, the total time available is:
\[ 6 \text{ hours/week} \times 5 \text{ weeks} = 30 \text{ hours} \]

### Step 3: Set Up the Time Inequality
Each non-calculator test takes 3 hours to create, and each calculator test takes 4 hours. The total time spent on creating the tests must be less than or equal to 30 hours. This can be expressed as:
\[ 3N + 4C \leq 30 \]

### Step 4: Set Up the Test Quantity Inequality
The teacher wants to provide at least 8 practice tests. This means the total number of tests (both non-calculator and calculator) must be at least 8. This can be expressed as:
\[ N + C \geq 8 \]

### Step 5: Write the System of Inequalities
Combining the inequalities from steps 3 and 4, we have the following system of inequalities:
1. \( N + C \geq 8 \)
2. \( 3N + 4C \leq 30 \)

### Conclusion
The system of inequalities that can help the teacher determine how many of each type of test she can create is:
\[ \begin{align*} N + C & \geq 8 \\ 3N + 4C & \leq 30 \end{align*} \]