a theater seating 300 charges $1 for children $2 for students and $5 for adult half as many adult and children and students areceipt totaled $800 how many children aattend

It would help if you proofread your questions before you posted them. "half as many adult and children and students"?

Are all the seats sold?

To find the number of children who attended the theater, we can set up an equation based on the given information.

Let's denote the number of children as "C." Since the theater charges $1 for each child, the total revenue from children would be $1 multiplied by the number of children, which gives us a total of C * 1 = C.

Similarly, for the students, the theater charges $2 for each student, so the total revenue from students would be $2 multiplied by the number of students. Since the problem states that there were half as many students as children, we can represent the number of students as C / 2. Therefore, the total revenue from students would be (C / 2) * 2 = C.

Finally, for the adults, the theater charges $5 for each adult, and the problem states that there were half as many adults as children. So, the number of adults can be represented as C / 2. The total revenue from adults would then be (C / 2) * 5 = 5C / 2.

Adding up the revenue from children, students, and adults, we get C + C + 5C / 2, which must equal $800 according to the problem.

We can now solve the equation to find the value of C for the number of children:
C + C + 5C / 2 = 800.

Combining like terms, we have:
(2C + 2C + 5C) / 2 = 800.

Simplifying further, we get:
9C / 2 = 800.

To isolate C, we can multiply both sides of the equation by 2/9:
C = (2/9) * 800.

Calculating this, we find:
C = 177.78 (rounded to the nearest whole number).

Therefore, approximately 178 children attended the theater.