Question

the logan county animal shelter has at most 4,310 square feet of space where it can house animals. each large animal must be given 25 square feet of space, and each small animal must be given 13 square feet. select the inequality in standard form that describes this situation. use the given numbers and the following variables. x = the number of large animals y = the number of small animals 25x + 13y ≤ 4,310 25x + 13y ≥ 4,310 25x + 13y > 4,310 25x + 13y < 4,310

Explanation:

Step1: Analyze space for large animals

Each large animal needs 25 sq ft, with \( x \) large animals, so space for large animals is \( 25x \) square feet.

Step2: Analyze space for small animals

Each small animal needs 13 sq ft, with \( y \) small animals, so space for small animals is \( 13y \) square feet.

Step3: Total space and inequality

Total space used by all animals is \( 25x + 13y \). The shelter has at most 4,310 sq ft, meaning total space used must be less than or equal to 4,310. So the inequality is \( 25x + 13y \leq 4310 \).

Answer:

\( 25x + 13y \leq 4310 \) (the first option: \( 25x + 13y \leq 4,310 \))