Let's assume that the theatre sold 8x adult tickets and 3x child tickets the day before the show, so the ratio of adult to child tickets sold was 8:3.
On the day of the show, the theatre sold 30 more adult tickets, so the total number of adult tickets sold became 8x + 30. The number of child tickets sold remained the same, so it was 3x.
The ratio of adult to child tickets sold on the day of the show was 7:2. So, we can write:
(8x + 30)/3x = 7/2
To solve for x, we can cross-multiply and simplify:
2(8x + 30) = 21x
16x + 60 = 21x
5x = 60
x = 12
Therefore, the theatre sold 8x adult tickets the day before the show, which is:
8x = 8(12) = 96 adult tickets.
So, the theatre sold 96 adult tickets and 3x child tickets (3 x 12 = 36) the day before the show, in the ratio 8:3.