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let a = the number of adult tickets sold
let c = the number of children tickets sold

so we know there were 200 sold so.....
a + c = 200

What does our next equation have to do with? (the first one was about how many people attended)

the next equation needs to deal with the profits being made... right?

Good.
each adult ticket cost 8.00 and each child cost 4.00 for a total of $1,304
so
8a + 4c = 1304

then solve for each?

a + c = 200
8a + 4c = 1304
do you know how to solve this system?

9a + 5c = 1504?

-8(a + c = 200)
8a + 4c = 1304
-8a - 8c = -1600
8a + 4c = 1304
now add these

-4c = -296?

which means that c = 74?

Yes... so substitute in
a + c = 200
a + 74 = 200
a = 126