Question

You are fishing for surfperch and rockfish, which are species of bottomfish. Gaming laws allow you to catch no more than 15 surfperch per day, no more than 10 rockfish per day, and no more than 20 total bottomfish per day.

a. Write a system of linear inequalities that represents the situation. Let x represent the number of surfperch and y represent the number of rockfish

Answer 1

Let
`\(x\)` represent the number of surfperch caught per day and
`\(y\)` represent the number of rockfish caught per day.

The conditions given are:

1. No more than 15 surfperch can be caught per day:

`\[ x \leq 15 \]`

2. No more than 10 rockfish can be caught per day:

`\[ y \leq 10 \]`

3. No more than 20 total bottomfish can be caught per day:

`\[ x + y \ \]leq 20`

Therefore, the system of linear inequalities representing the situation is:

`\[ \begin{cases} x \leq 15 \\ y \leq 10 \\ x + y \leq 20 \end{cases} \]`