Question

Which system of equations models the following problem if x represents the number of parrotfish Jenna bought, and y represents the number of triggerfish she bought?

\[ \begin{cases}
x + y = 280 \\
y = 4x
\end{cases} \\
1. \( \begin{cases}
x, y = 280, 4x
\end{cases} \)
2. \( \begin{cases}
x, y = 4, 280x
\end{cases} \)
3. \( \begin{cases}
x + 4y = 280 \\
y = 4x
\end{cases} \)
4. \( \begin{cases}
x - y = 280 \\
y = 4x
\end{cases} \)

Answer 1

The correct system of equations for the scenario where x is the number of parrotfish and y is the number of triggerfish Jenna bought is: Option 3, which includes the equations x + 4y = 280 and y = 4x.

Step-by-step explanation:

The system of equations that models the problem where x represents the number of parrotfish Jenna bought, and y represents the number of triggerfish she bought is:

1. x + y = 280
2. y = 4x

The correct answer to the student's question is Option 3:

\begin{cases}
x + 4y = 280 \\
y = 4x
\end{cases}

This represents a system of linear equations where the first equation sums the total number of fish bought, and the second equation gives the relation between the number of triggerfish and parrotfish.