Answer:
276 children and 488 adults attended.
Step-by-step explanation:
The problem details that the total number of people, which includes adults and children, is 764.
This means that if x represents the number of children and y for the adults the equation form is,
[tex]x+y=764[/tex].
The problem also says that each child gets 2 slices, adults get 5 per and that the total number of slices is 2992. This description equates to,
[tex]2x+5y=2992[/tex].
We can rewrite x in terms of y, solve for y and plug that value back into either equation to find the x value!
[tex]x+y=764\Longrightarrow x=764-y[/tex]
[tex]2(764-y)+5y=2992[/tex]
[tex]1528-2y+5y=2992[/tex]
[tex]3y+1528=2992[/tex]
[tex]3y=1464[/tex]
[tex]y=488[/tex]
Solving for x, we can plug the y-value into the rearranged first equation of the system.
[tex]x=764-(488)=276[/tex]
So, there were 276 children and 488 adults.