A high school has a `$1000` budget to buy calculators. Each scientific calculator will cost the school `$12.97` and each graphing calculator will cost the school `$73.89`. Which of the following inequalities represents the possible number of scientific calculators S and graphing calculators G that the school can purchase while staying within their specified budget?

Options

A. `12.97S+73.89G gt 1000`
B. `12.97S+73.89G le 1000`
C. `(12.97)/(S)+(73.89)/(G) ge 1000`
D. `(12.97)/(S)+(73.89)/(G) le 1000`

Answer

To solve the problem, we need to establish an inequality that represents the total cost of purchasing scientific and graphing calculators within the school's budget.

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( S \) be the number of scientific calculators.
- Let \( G \) be the number of graphing calculators.

2. **Identify Costs**:
- The cost of one scientific calculator is \( 12.97 \) dollars.
- The cost of one graphing calculator is \( 73.89 \) dollars.

3. **Calculate Total Costs**:
- The total cost for \( S \) scientific calculators is \( 12.97S \).
- The total cost for \( G \) graphing calculators is \( 73.89G \).

4. **Set Up the Inequality**:
- The total cost of both types of calculators must be less than or equal to the budget of \( 1000 \) dollars. Therefore, we can write the inequality:
\[ 12.97S + 73.89G \leq 1000 \]

5. **Final Inequality**:
- The inequality that represents the possible number of scientific calculators \( S \) and graphing calculators \( G \) that the school can purchase while staying within their specified budget is:
\[ 12.97S + 73.89G \leq 1000 \]