The Mayflower Diner has a rule that dessert pies must be sliced so that the angle at the tip of a piece of pie (where the tip is at the center of the pie ) lies between 20 and 30 degrees . Which of the following inequalities can be used to determine whether an angle a at the tip of a pie slice satisfies the rule ?

Options

A. |a - 25 | lt 5
B. |a-25| lt 20
C. |a-25| lt 30
D. |a| lt 30

Answer

To determine the appropriate inequality that represents the rule for the angle at the tip of a pie slice at the Mayflower Diner, we need to analyze the given conditions step by step.

### Step-by-Step Solution:

1. **Understand the Condition**: The angle \( A \) at the tip of a pie slice must lie between 20 degrees and 30 degrees. This can be expressed as:
\[ 20 < A < 30 \]

2. **Rearranging the Condition**: We want to express this condition in terms of an absolute value inequality. To do this, we can find a central value and the deviation from that value. The midpoint between 20 and 30 is 25. The deviation from 25 to either boundary (20 or 30) is 5 degrees.

3. **Formulating the Absolute Value Inequality**: The condition can be rewritten using absolute values:
\[ |A - 25| < 5 \]
This inequality states that the distance of \( A \) from 25 must be less than 5 degrees, which corresponds to the range of 20 to 30 degrees.

4. **Verification of Options**:
- **Option A**: \( |A - 25| < 5 \) translates to \( 20 < A < 30 \) (this satisfies the condition).
- **Option B**: \( |A - 25| < 20 \) translates to \( 5 < A < 45 \) (this does not satisfy the condition).
- **Option C**: \( |A - 25| < 30 \) translates to \( -5 < A < 55 \) (this does not satisfy the condition).
- **Option D**: \( |A| < 30 \) translates to \( -30 < A < 30 \) (this does not satisfy the condition).

5. **Conclusion**: The only option that satisfies the rule of the Mayflower Diner is:
\[ \text{Option A: } |A - 25| < 5 \]