please help me asap

Question

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.

A.x > 0 and y > 0 

B.0 < x ≤ 12 and 0 < y ≤ 36

C.0 < x ≤ 12 and y > 36

D.x > 0 and y < 23

Answer 1

Based on the description we have two facts:

1. The number of female gazelles X cannot exceed 12, therefore X ≤ 12
2. The number of male gazelles Y MUST be at least three times the value of X, therefore Y ≥ 3X

Solution C is the only answer that ALWAYS satisfies these conditions. Solution B appears to be correct, and is true in some cases for values of X and Y, but is NOT always true. For example:

Solution B has logic that would allow for values of X = 8 and Y = 16, however in this instance Y ≠ 3X., Y < 3X (16 < 24)

Solution C is the only answer that both satisfies the quantity of female gazelles is less than or equal to 12 (0 < X ≤ 12) and also guarantees the gazelle population will thrive (Y ≥ 3X).