One night, the movie theater sold 715 movie tickets. The ticket prices are shown in the table below. In all, $3,786.50 was taken in. How many of each kind of ticket were sold at the movies? Show your work.

Question

anonymous · Answer

attachment

briana.img · Answer

a + c = 715 ---->(a = 715 - c) 6.50a + 3.50c = 3786.50
 now sub 715 - c in for a in the 2nd equation

briana.img · Answer

a + c = 715 --- adult + child = 715 tickets
6.50a + 3.50c = 3786.50 -- 6.50 adult tickets + 3.50 child tickets = 3786.50

a + c = 715 --> a = 715 - c
now we sub

6.50a + 3.50c = 3786.50
6.50(715 - c) + 3.50c = 3786.50 --- distribute through the parenthesis
4647.50 - 6.50c + 3.50c = 3786.50 -- subtract 4647.50
-6.50c + 3.50c = 3786.50 - 4647.50 -- combine like terms
-3c = - 861
c = 287

a + c = 715 
a + 287 = 715
 a = 715 - 287 
a = 428

check.. 6.50(428) + 3.50(287) = 3786.50 
2782 + 1004.50 = 3786.50
3786.50 = 3786.50 (correct) 

adult tickets (a) = 428 
child ticlets (c) = 287

anonymous · Answer

wow thanks that helped so much!! I understand now