Let's work through the problem step-by-step to determine the correct answer.
1. Determine the Current Number of Animals in the Shelter:
- Currently, the shelter has 165 animals.
2. Determine the Shelter's Maximum Occupancy:
- The shelter's maximum occupancy is 300 animals.
3. Calculate the Number of Additional Animals the Shelter Can Take In:
- To find out how many more animals the shelter can take before reaching the maximum occupancy, subtract the current number of animals from the maximum occupancy:
[tex]\[
300 - 165 = 135
\][/tex]
So, the shelter can take in [tex]\( 135 \)[/tex] more animals.
4. Calculate the Number of Days the Shelter Can Continue Taking in Animals:
- The shelter takes in an average of 5 animals per day. To determine how many days [tex]\( x \)[/tex] the shelter can keep taking in animals without exceeding the limit, divide the number of additional animals by the daily intake:
[tex]\[
x = \frac{135}{5} = 27
\][/tex]
So, the shelter can continue taking in animals for [tex]\( 27 \)[/tex] days before reaching the maximum occupancy.
5. Determine the Correct Inequality:
- We need to find the inequality that represents this condition. Since the shelter reaches its maximum capacity after exactly [tex]\( 27 \)[/tex] days, the inequality should be:
[tex]\[
x < 33
\][/tex]
because 27 is less than 33 and the problem specifies that the inequality should represent the continued intake without exceeding the limit, which means [tex]\( x \)[/tex] should be less than 33 days.
Therefore, the correct answer is:
C. [tex]\( x < 33 \)[/tex]
