10 adults and 5 children can watch a movie for 75 dollars. but 8 adults and 10 children can watch the movie for 78 dollars. how much would it cost for 6 adults and 10 children to watch the movie

10 adults + 5 children = $75 (1)
8 adults + 10 children = $78  (2)

(1) x 2 : 20 adults + 10 children = $150  (1a)

(1a) - (2) : 12 adults = $72
                   1 adult  =  $6

Substitute 1 adult = $6 into (1):

10 ($6) + 5 children = $75
$60 + 5 children = $75
5 children = $15
1 child = $3

Therefore 1 adult = $6  and 1 child = $3

Find 6 adult and 10 children: 
6 adults + 10 children = 6(6) + 10(3) = 36 + 30 = $66

$66