Question

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?

Answer 1

`x+y=138`

`4x+8y=1020`

system of equations is used.

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

Explanation:

Given:

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
`x.`

And let the number of adults went to premiere be
`y.`

So, total number of adults and children attended:

`x+y=138\\\\y=138-x\ \ \ ....(1)`

Now, the total amount made in ticket sales:

`4(x)+8(y)=1020`

So, we use

`x+y=138`

`4x+8y=1020`

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

Substituting the value of
`y` in equation (1):

`4(x)+8(138-x)=1020`

`4x+1104-8x=1020\\\\1104-4x=1020`

Subtracting both sides by 1104 we get:

`-4x=-84`

Dividing both sides by -4 we get:

`x=21.`

The number of children went to premiere = 21.

Now, substituting the value of
`x` in equation (1):

`y=138-x\\\\y=138-21\\\\y=117.`

The number of adults went to premiere = 117.

Hence,

`x+y=138`

`4x+8y=1020` system of equations is used.

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