Answer: 275 adult tickets and 500 children's tickets were sold.

Step-by-step explanation:

Let a represent the number of adult tickets that were sold.

Let c represent the number of children's tickets that were sold.

The total number of tickets that were sold is 775. It means that

a + c = 775

If adults tickets sold for 2.50 and children’s tickets sold for 1.00 and the total amount was $1187.5, it means that

2.5a + c = 1187.5- - - - - - - - - - -1

substituting a = 775 - c into equation 1, it becomes

2.5(775 - c) + c = 1187.5

1937.5 - 2.5c + c = 1187.5

- 2.5c + c = 1187.5 - 1937.5

- 1.5c = - 750

c = - 750/ - 1.5

c = 500

Substituting c = 500 into a = 775 - c, it becomes

a = 775 - 500

a = 275