College

Select the correct answer.

Kevin is baking bread for a family function. The initial temperature of the oven is twice the room temperature. He knows that yeast, a key ingredient, thrives within the temperature range of [tex]$90^{\circ} F$[/tex] to [tex]$95^{\circ} F$[/tex]. To facilitate yeast growth, Kevin decreases the temperature of the oven by [tex]$44^{\circ} F$[/tex].

Which inequality represents the given situation?

A. [tex]90 \leq 2x + 44 \leq 95[/tex]
B. [tex]90 \leq 2x - 44 \leq 95[/tex]
C. [tex]90 \geq 2x - 44 \leq 95[/tex]
D. [tex]90 \geq 2x + 44 \leq 95[/tex]

Answer :

Sure! Let's go through the problem step by step.

1. Identify Room and Oven Temperature Relationships:
- Let [tex]\( x \)[/tex] represent the room temperature.
- According to the question, the initial temperature of the oven is twice the room temperature. So, the initial oven temperature can be expressed as [tex]\( 2x \)[/tex].

2. Adjust the Oven Temperature:
- Kevin decreases the oven temperature by [tex]\( 44^{\circ} F \)[/tex].
- So, the new temperature of the oven is [tex]\( 2x - 44 \)[/tex].

3. Temperature Range for Yeast Growth:
- The yeast needs to thrive within the range of [tex]\( 90^{\circ} F \)[/tex] to [tex]\( 95^{\circ} F \)[/tex].

4. Establish the Inequality:
- Since the yeast must grow in that specific range, the inequality representing the situation is:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
- This inequality ensures that the adjusted oven temperature falls within the optimal range for yeast growth.

5. Select the Correct Answer:
- From the options provided, option B matches our derived inequality:
- B. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex]

Thus, the correct inequality that represents the given situation is option B.