Question

Which system of equations models this problem? 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?

a) {x+y=405 y=8x
b) {x+4y=8 y=405x
c) {x−y=405 y=8x
d) {x+y=8 y=405x

Answer 1

A x+y=405

y=8x

Explanation:

I took the test.

Answer 2

a) {x+y=405 y=8x

Explanation:

Notation

X= represents the number of angelfish Carlos bought

Y= represents the number of parrotfish he bought.

Total of fish =405

He bought 8 times as many parrotfish as angelfish

Solution to the problem

The correct system of equations are:

a) {x+y=405 y=8x

Since the addition of x+y=405 , since 405 represent the total os fishes. And the claim that "He bought 8 times as many parrotfish as angelfish" is expressed on the equation y=8x.

Now we can solve the equation, we can use for example the substitution method, let's name the equations like this:

x+y=405 (1)

y=8x (2)

If we solve x from equation (1) we got:

x=405-y (3)

And if we replace equation (3) into equation (2) we got:

y=8(405-y)=3240-8y[/tex]

And now we can solve for y like this:

`9y=3240`, so then y =360

And replacing into equation (3) we got the value of x

`x=405-360=45`

And we can check that we satisfy the two conditions:

x+y=360+45=405

y=8(45)=360