Select the correct answer.
An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals.
If none of the animals get adopted, which inequality represents how many more days, $x$, the shelter can continue to take in animals without exceeding its occupancy limit?
A. $x<25$
B. $x<27$
C. $x<33$
D. $x<35
Answer (1)
• Define x as the number of days the shelter can continue taking in animals. • Set up the inequality: 165 + 5 x < 300 .
• Solve the inequality: 5 x < 135 , which simplifies to x < 27 .
• The shelter can continue to take in animals for fewer than 27 days: x < 27 .
Explanation
Setting up the Inequality Let x be the number of days the shelter can continue to take in animals. The shelter takes in 5 animals per day, so after x days, the shelter will have taken in 5 x animals. The shelter currently has 165 animals. The total number of animals after x days will be 165 + 5 x . The shelter must keep its total occupancy below 300, so we have the inequality 165 + 5 x < 300 .
Isolating the Variable Term To solve the inequality 165 + 5 x < 300 , we first subtract 165 from both sides:
165 + 5 x − 165 < 300 − 165
5 x < 135
Solving for x Now, we divide both sides by 5:
5 5 x < 5 135
x < 27
Finding the Correct Answer The inequality that represents how many more days, x , the shelter can continue to take in animals without exceeding its occupancy limit is x < 27 . Therefore, the correct answer is B.
Examples
Imagine you're managing a library. Each week, 50 new books arrive. The library can hold a maximum of 2000 books. Currently, you have 1200 books. This problem helps you determine how many weeks you can continue receiving new books without exceeding the library's capacity. Understanding inequalities helps in managing resources and planning for future needs in various real-life scenarios.
