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$x < 35$

Question

05-11-2026
Mathematics

Answered

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$x < 35$

Verified Answer :

Related Questions

Which is the name of C5H12 nheptane nbutane All of these npentane nhexane

What do the encomienda mita and debt peonage have in common a They were all social systems of discriminating between various racial combinations found in Iberia

Which would have the GREATEST effect on the rate of photosynthesis in a plant A oxygen level B light intensity C sugar concentration D starch concentration

Can someone unscramble the letters ASPOLRA and what word does it make

show all the ways to make 34 as tens and ones

Please hurry why are some Americans opposed to trust A they eliminated compitition and drove up prises for consumers B they improvedd efficiently C they created

The shorter side of a triangle ABC is half of the second side and a third of the longest side how does the perimeter of the triangle compared to the longest sid

Find the mean and the median of 6 5 3 28 6 4 7

A common characteristic of a fad diet is that it claims to

which unit would you use to mesure the thickness of a coin

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T15:48:00-05:00

Define the total occupancy after $x$ days as $165 + 5x$.
Set up the inequality $165 + 5x < 300$ to represent the shelter's capacity limit.
Solve the inequality by subtracting $165$ from both sides and then dividing by $5$.
The resulting inequality is $x < 27$, which matches the second option.
Final answer: $\boxed{x < 27}$

Explanation

Analyzing the Problem Data and Setting up the Inequality

To determine the number of days $x$ the animal shelter can continue to take in animals, we must first model the total occupancy as a function of time. We know the following:

The current occupancy is $165$ animals.
The shelter takes in an average of $5$ animals per day.
The total occupancy after $x$ days will be the initial occupancy plus the number of new animals admitted, which is $5 \times x$.
The total occupancy must remain strictly less than $300$.

Therefore, the total occupancy after $x$ days is given by the expression $165 + 5x$. To ensure the shelter does not exceed its limit, we set this expression to be less than $300$.

Solving the Inequality for x

We start with the inequality:
\[165 + 5x < 300\]
To solve for $x$, we first subtract the current occupancy, $165$, from both sides of the inequality:
\[5x < 300 - 165\]
\[5x < 135\]
Next, we isolate $x$ by dividing both sides of the inequality by $5$:
\[x < \frac{135}{5}\]
Performing the division:
\[x < 27\]
This inequality shows that the shelter can continue to take in animals for any number of days strictly less than $27$.

Selecting the Correct Inequality

Comparing our result, $x < 27$, with the given options:

$x < 25$
$x < 27$
$x < 33$
$x < 35$

The correct option is $x < 27$.

Examples

This type of modeling is very useful in everyday logistics, such as tracking inventory in a warehouse or managing space in a parking garage. By understanding the current capacity and the rate at which items are being added, you can accurately predict how much time you have before reaching your maximum limit. For example, if a garage has $50$ spaces and adds $2$ cars per hour, and currently has $30$ cars, the inequality $30 + 2x < 50$ helps determine when the garage will be full.