High School

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

Answer :

To solve this problem, we need to figure out which inequality correctly represents the situation described.

1. Understand the problem:
- The initial temperature of the oven is twice the room temperature. Let's denote the room temperature as [tex]\( x \)[/tex].
- The oven temperature after being decreased by 44 degrees should be suitable for yeast growth, which is between 90°F and 95°F.

2. Set up the situation mathematically:
- Initial oven temperature is [tex]\( 2x \)[/tex].
- After reducing the temperature by 44°F, the oven temperature becomes [tex]\( 2x - 44 \)[/tex].

3. Write the inequality to cover the range for yeast growth:
- The resulting oven temperature should be between 90°F and 95°F, so the inequality is:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]

This inequality ensures that after reducing the oven temperature by 44 degrees, it still falls within the optimal range for yeast growth.

Therefore, the correct choice is D: [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex].