Question

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?
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?
\\(\

$$\begin{cases} x - y = 420 \\\\ y = 6x \\end{cases}$$

\\)
\\(\

$$\begin{cases} x + 6y = 420 \\\\ y = 6x \\end{cases}$$

\\)
\\(\

$$\begin{cases} x + y = 6 \\\\ y = 420x \\end{cases}$$

\\)
\\(\

$$\begin{cases} x + y = 420 \\\\ y = 6x \\end{cases}$$

\\)

Explanation:

Step1: Identify correct equation system

We know total fish = 420, so $x + y = 420$. Parrotfish ($y$) are 6× angelfish ($x$), so $y=6x$. The correct system is

$$\begin{cases} x + y = 420 \\ y = 6x \end{cases}$$

Step2: Substitute $y=6x$ into total

Substitute $y=6x$ into $x+y=420$:
$x + 6x = 420$
$7x = 420$

Step3: Solve for $x$

Calculate $x$:
$x = \frac{420}{7} = 60$

Step4: Solve for $y$

Use $y=6x$:
$y = 6 \times 60 = 360$

Answer:

Correct system: $\boldsymbol{

$$\begin{cases} x + y = 420 \\ y = 6x \end{cases}$$

}$
Number of angelfish ($x$): 60
Number of parrotfish ($y$): 360