A zookeeper is monitoring the population of gazelles. The herd needs three times more males than females to thrive, and the zoo only has room for 12 female gazelles. Let x = the number of female gazelles and y = the number of male gazelles. Write the constraints to represent a thriving population of gazelles at the zoo. x > 0 and y > 0 0 < x ≤ 12 and 0 0 and y < 23

0 < x ≤ 12 and 0 < y ≤ 36

Step-by-step explanation:

Here, x represents the number of female gazelles and y represents the number of male gazelles.

The zoo only has room for 12 female gazelles.

∵ The number of rooms must be more than or equal to the total female gazelles,

12 ≥ x

Also, number of animals can not be negative,

And, it must be greater than 0.

⇒ 0 < x ≤ 12,

⇒ 3 (0) < 3x ≤ 3 (12)

⇒ 0 < 3x ≤ 36

∵ Number of males gazelles = 3 * number of female gazelles

⇒ y = 3x

⇒ 0 < y ≤ 36

Hence, the constraints to represent a thriving population of gazelles at the zoo are,

0 < x ≤ 12,

0 < y ≤ 36