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. x > 0 and y > 0 0 < x ≤ 12 and 0 < y ≤ 36 0 < x ≤ 12 and y > 36 x > 0 and y < 23

Answer 1

The constraint which represent a thriving population of gazellea at the zoo is:

0 < x ≤ 10 and 0 < y ≤ 30.

Explanation:

Let x = the number of female gazelles and y = the number of male gazelles.

Now, it is given that:

The group needs two times more males than females to thrive, and the zoo only has room for 12 female gazelles.

This means that:

0 < x ≤ 10

( Because there are no room for more than 12 gazelles )

Also,

y= 3x

Since,

x>0

This means that: 3x>0

i.e. y>0

and x ≤ 12

i.e. 2x ≤ 30

i.e. y ≤ 30

Hence, the constraints which represent a thriving population of gazelles

at the zoo is:

0 < x ≤ 12 and 0 < y ≤ 30.

Answer 2

0 < x ≤ 12 and 0 < y ≤ 36

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