To solve this problem we can use system of equations.
First equation can be
321=x+y
where x - ppl between 4-17 and y - adult
second equation can be as follows
1590=6y+4x
So we have
\(\left \{ {{321=x+y} \atop {1590=6y+4x}} \right.\)
From first equation we get value of x in times of y
x=321-y
Now we can substitute it into second eq.
1590=6y+4(321-y)
now simply if
1590=6y+1284-4y /-1284 both sides
306=2y /:2 divide both sides by 2
y=153
Now we can back substitude
x=321-153
x=168
So we get result
\(\left \{ {{y=153 - adult} \atop {x=168 - kids}} \right.\)