Question

create a system of equations to represent this situation. be sure to explain the meaning of each variable. graph the system of equations. determine the break even point for Chuck E Cheese and Bright Child, Adventure Plex and Bright Child, Adventure Plex and Chuck E Cheese.

Answer 1

For them, let x = number of children of the party and

A=Adventure Plext cost

B= Bright Child cost

C= Chuck E Cheese cost

So,

`\begin{gathered} A=300+12x \\ B=180+15x \\ C=18x \end{gathered}`

Then, graphing each equation of the system of equations

Now, for determine the break even point for Chuck E Cheese and Bright Child you have

`\begin{gathered} 180+15x=18x \\ 180=18x-15x \\ 180=3x \\ (180)/(3)=x \\ 60=x \end{gathered}`

That is, the break even point for Chuck E Cheese and Bright Child occurs when x = 60 children.

For determine the break even point for Adventure Plex and Bright Child you have

`\begin{gathered} 300+12x=180+15x \\ 300+12x-180=180+15x-180 \\ 120+12x=15x \\ 120+12x-12x=15x-12x \\ 120=3x \\ (120)/(3)=(3x)/(3) \\ 40=x \end{gathered}`

That is, the break even point for Adventure Plex and Bright Child occurs when x = 40 children.

Finally, For determine the break even point for Adventure Plex y Chuck E Cheese you have

`\begin{gathered} 300+12x=18x \\ 300+12x-12x=18x-12x \\ 300=6x \\ (300)/(6)=(6x)/(6) \\ 50=x \end{gathered}`

That is, the break even point for Adventure Plex and Chuck E Cheese occurs when x = 50 children.