Question

Carlos bought a total of 405 fish for a museum display. He bought parrotfish and angelfish. He bought 8 times as many parrotfish as angelfish. Let the variable x represent the number of angelfish Carlos bought and the variable y represent the number of parrotfish he bought. Use a system of equations to model and solve this situation. What is the solution to the system of equations? (60, 345) (45, 360) (55, 350) (35, 370)

Answer 1

x+y=405

x=8y

plug it into the first equation

8y+y=405

9y=405

y=45

now we can plug it back into x+y=405

x+45=405

x=360

The answer is (45, 360)

Answer 2

Solution to the system of equations $y=8x,x+y=405$ is $(45,360)$

An equation is said to be linear equation in two variables if it is written in the form of $ax+by+c=0$, where $a,b,c$ are real numbers and the coefficients $a,b$are not equal to zero.

Let the variable $x$ represent the number of angelfish Carlos bought and the variable $y$ represent the number of parrotfish he bought.

Carlos bought $8$ times as many parrotfish as angelfish.

$y=8x$

Carlos bought a total of 405 fish for a museum display.

$x+y=405$

Put $y=8x$

$x+8x=405$

      $9x=405$

        $x=45$

So,

$y=8(45)$

   $=360$

Solution to the system of equations is $(45,360)$

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