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]$90 \geq 2x + 44 \leq 95$[/tex]

B. [tex]$90 \leq 2x - 44 \leq 95$[/tex]

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

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

Answer :

To solve this problem, let's carefully look at the situation.

1. Initial Condition:
- The initial temperature of the oven is twice the room temperature. Let's call the room temperature [tex]\( x \)[/tex].
- Therefore, the initial oven temperature can be expressed as [tex]\( 2x \)[/tex].

2. Adjustment for Yeast:
- Kevin needs to lower the oven's temperature by 44 degrees to create a suitable environment for yeast.
- This means the adjusted oven temperature is [tex]\( 2x - 44 \)[/tex].

3. Yeast Growth Range:
- Yeast thrives between [tex]\( 90^{\circ} F\)[/tex] and [tex]\( 95^{\circ} F\)[/tex].

With these details, you can set up an inequality based on the adjusted oven temperature:

[tex]\[ 90 \leq 2x - 44 \leq 95 \][/tex]

This inequality ensures that the adjusted oven temperature is within the optimal range for yeast activity.

Now, let's check which option correctly represents this inequality:

- Option B: [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex]

This matches our setup, so Option B correctly represents the situation.

Thus, the proper inequality for this situation is:

[tex]\[ 90 \leq 2x - 44 \leq 95 \][/tex] which is Option B.