AC Lim has done a good job of presenting his solutions.

I will do up my solutions as an alternative (different from AC Lim's, but closely related).

You need to realise what is happening. As far as we can, we try to make a certain quantity become a fixed number.

Here, there are 200 more children than adults. Nope, the number of children and adults are not the same. Neither is the pricing.

What if...all of a sudden, 200 further adults joined the theme park? What happens to the number of children and adults? Think for a moment...

If 200 new adults suddenly join in, then there would be the same number of children and adults. This becomes much easier to compute later on.

But with 200 new adults joining in, more money will be collected by the theme park. But how much?

$45.50 x 200 = $9 100

The park could have collected $9 100 more because of these 200 extra adults.

$21 950 + $9 100 = $31 050

For a certain equal number of children and adults, the total amount of money collected by the theme park is $31 050.

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Let's group one child and one adult into one "group".

Then, in one "group", the total cost of the two tickets (one adult and one child)
= $45.50 + $23.50
= $69

How many such "groups" would we need, then?

$31 050 / $69 = 450

We would need 450 of such groups for the total money collected to be $31 050. But one group contains one child (and no new child "joined" further).

So, there must have been 450 children in the theme park.

For such questions, I try to make the number of "children" and the number of "adults" to be equal so that I can group them later on. This is done by tweaking the story a little as what I have done.

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Some alternative questions which have similar ideas to this can be like this.

"A pen cost $2 and a book cost $10.
I bought two more pens than books.
I paid $88 altogether.
How many pens did I buy?"

"A truck has a mass of 1 500 kg.
A car has a mass of 1 000 kg.
There were two more cars than trucks in a car park and no other vehicles were present.
The total masses of these vehicles is 32 000 kg.
How many trucks were there?"

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Or a more challenging version of a similar grouping idea:

"A pen cost $2 and a book cost $10.
I bought twice as many pens as books.
I paid $168 altogether.
How many pens did I buy?"

Thx