To find how many more days the shelter can continue to take in animals without exceeding its occupancy limit, given the shelter's current number of animals and its capacity, let's solve the problem step-by-step.
1. Understand the total capacity and current number of animals:
- The shelter has a maximum occupancy limit of 300 animals.
- Currently, there are 165 animals in the shelter.
2. Determine additional capacity available:
- Calculate how many more animals the shelter can accommodate:
[tex]\[
\text{Additional capacity} = \text{Maximum occupancy} - \text{Current number of animals}
\][/tex]
[tex]\[
\text{Additional capacity} = 300 - 165 = 135
\][/tex]
So, the shelter can take in 135 more animals.
3. Calculate the number of days the shelter can continue to accept animals:
- The shelter takes in an average of 5 animals per day.
- To determine how many days (let's denote it by [tex]\( x \)[/tex]) the shelter can continue to accept animals without exceeding its limit, use the equation:
[tex]\[
5x \leq 135
\][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[
x \leq \frac{135}{5}
\][/tex]
[tex]\[
x \leq 27
\][/tex]
- The largest integer value of [tex]\( x \)[/tex] that satisfies this inequality is 27, but since the inequality is strict (the shelter must keep its total occupancy below 300 animals), we write it as:
[tex]\[
x < 27
\][/tex]
So, the inequality representing how many more days [tex]\( x \)[/tex] the shelter can continue to take in animals without exceeding its occupancy limit is:
[tex]\[
x < 27
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x < 27 \)[/tex]
