Question

a pet shop sells zebrafish and angelfish, which can coexist in the same tank for display. the shops owner wants to keep them on display in the front of the shop under the following constraints: no more than 30 fish can be in the tank at the same time. (if there are more than 30, the extras will live in another tank in the shop.) the number of angelfish must be less than the number of zebrafish. there should be at least 5 zebrafish in the tank. let x represent the number of zebrafish, and y represent the number of angelfish. what system of inequalities models this situation? select the three that apply.
□ y ≤ x
□ x ≥ 5
□ x + y < 30
□ x + y ≤ 30
□ x ≤ 5
□ y < x

Explanation:

Step1: Translate total fish constraint

The tank can hold no more than 30 fish, meaning the sum of zebrafish ($x$) and angelfish ($y$) is less than or equal to 30.
$x + y \leq 30$

Step2: Translate angelfish count constraint

The number of angelfish must be less than the number of zebrafish.
$y < x$

Step3: Translate zebrafish minimum constraint

There must be at least 5 zebrafish, so $x$ is greater than or equal to 5.
$x \geq 5$

Answer:

B. $x \geq 5$
D. $x + y \leq 30$
F. $y < x$