Mega Movies hosted a film premiere on Friday night. They charged $8 for adults and $4 for children. One hundred thirty-eight adults and children attended, and $1,020 was made in ticket sales. Which system of equations below can be used to determine how many children and how many adults went to the film premiere?

Mega Movies hosted a film premiere on Friday night. They charged $8 for adults and $4 for children. One hundred thirty-eight adults and children attended, and $1,020 was made in ticket sales.

Now, to find the children and adults went to the film premiere.

Let the number of children went to premiere be [tex]x.[/tex]

And let the number of adults went to premiere be [tex]y.[/tex]

So, total number of adults and children attended:

[tex]x+y=138\\\\y=138-x\ \ \ ....(1)[/tex]

Now, the total amount made in ticket sales:

[tex]4(x)+8(y)=1020[/tex]

So, we use

[tex]x+y=138[/tex]

[tex]4x+8y=1020[/tex]

system of equations to find the number of children and adults.

Substituting the value of [tex]y[/tex] in equation (1):

[tex]4(x)+8(138-x)=1020[/tex]

[tex]4x+1104-8x=1020\\\\1104-4x=1020[/tex]

Subtracting both sides by 1104 we get:

[tex]-4x=-84[/tex]

Dividing both sides by -4 we get:

[tex]x=21.[/tex]

The number of children went to premiere = 21.

Now, substituting the value of [tex]x[/tex] in equation (1):

[tex]y=138-x\\\\y=138-21\\\\y=117.[/tex]

The number of adults went to premiere = 117.

Hence,

[tex]x+y=138[/tex]

[tex]4x+8y=1020[/tex] system of equations is used.

There are 21 children and 117 adults went to the film premiere.