A movie theater charges $8 for children tickets and $12 for adult tickets. A total of 110 tickets were sold for $1200. How many of each ticket type were sold?

30 children tickets and 80 adult tickets were sold.

Step-by-step explanation:

Let x represent the number of children tickets that were sold.

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

A total of 110 tickets were sold. It means that

x + y = 110

The movie theater charges $8 for children tickets and $12 for adult tickets. The total sales from the tickets was $1200. It means that

8x + 12y = 1200- - - - - - - - - 1

Substituting x = 110 - y into equation 1, it becomes

8(110 - y) + 12y = 1200

880 - 8y + 12y = 1200

- 8y + 12y = 1200 - 880

4y = 320

y = 320/4

y = 80

x = 110 - y = 110 - 80

x = 30

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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