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?

Question

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.