Which system of equations models the following problem if x represents the number of angelfish Yves bought and y represents the number of parrotfish he bought?

Question

Yves bought 420 tropical fish for a museum display. He bought 6 times as many parrotfish as angelfish. How many of each type of fish did he buy?

Answer 1

To model the problem as a system of equations, we can use the information given:

1. Yves bought a total of 420 tropical fish. This can be represented by the equation: \[ x + y = 420 \] where \( x \) is the number of angelfish and \( y \) is the number of parrotfish.

2. Yves bought 6 times as many parrotfish as angelfish. This can be represented by the equation: \[ y = 6x \]

Combining these two equations gives us the system of equations: \[ \begin{cases} x + y = 420 \ y = 6x \end{cases} \]

This system can be solved to find the values of \( x \) and \( y \).