Question

Which system of equations models the following problem if x represents the number of angelfish Nancy bought and y represents the number of goldfish she bought?

Nancy bought 360 tropical fish for a museum display. She bought 8 times as many goldfish as angelfish. How many of each type of fish did she buy?

Responses

{x+y=8y=360x
System of equations. First equation. x plus y equals 8. Second equation. y equals 360 x.

{x+y=360y=8x
System of equations. First equation. x plus y equals 360. Second equation. y equals 8 x.

{x−y=360y=8x
System of equations. First equation. x minus y equals 360. Second equation. y equals 8 x.

{x+8y=360y=8x

Answer 1

Let's define the variables based on the problem description:

- Let \( x \) represent the number of angelfish Nancy bought.
- Let \( y \) represent the number of goldfish Nancy bought.

According to the problem:

1. Nancy bought a total of 360 tropical fish, which gives us the equation:
\[
x + y = 360
\]

2. She bought 8 times as many goldfish as angelfish, leading to the equation:
\[
y = 8x
\]

Now we can combine these equations. The system of equations that models the problem is:
\[
\begin{cases}
x + y = 360 \\
y = 8x
\end{cases}
\]

Looking at the given options, the correct choice is:
\[
\{x + y = 360, \, y = 8x\}
\]

This matches the response:
\[{x + y = 360, \, y = 8x}\]
So, Nancy bought 360 tropical fish total, and she bought 8 times as many goldfish as angelfish.