Question

The variable x represents the number of angelfish Carlos bought and the variable y represents the number of parrotfish he bought.

Carlos bought 405 tropical fish for a museum display. He bought 8 times as many parrotfish as angelfish.

How many of each type of fish did he buy?

Which system of equations models this problem?

Responses

{x+4y=8y=405x
left curly bracket. first line. x plus 4 y equals 8. second line. y equals 405 x

{x+y=405y=8x
left curly bracket. first line. x plus y equals 405. second line. y equals 8 x

{x−y=405y=8x
left curly bracket. first line. x minus y equals 405. second line. y equals 8 x

{x+y=8y=405x

Answer 1

To model the problem, we need to set up a system of equations based on the information given.

1. **Total Fish Equation**: Carlos bought a total of 405 tropical fish, so the equation is:
\[
x + y = 405
\]

2. **Parrotfish Equation**: He bought 8 times as many parrotfish as angelfish. Since \(y\) represents the number of parrotfish and \(x\) represents the number of angelfish, we can express this relationship as:
\[
y = 8x
\]

Now, we can combine these two equations to get the system:
1. \( x + y = 405 \)
2. \( y = 8x \)

Looking at the response options provided, the correct system of equations that models this problem is:

\[
\left\{ \begin{array}{l}
x + y = 405 \\
y = 8x
\end{array} \right.
\]

Thus, the correct answer is:
\[
\{x+y=405, y=8x\}
\]