Question 1204597
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Let's say there are 129 adults in attendance.


That would bring in 2.25*129 = 290.25 dollars in revenue. 
This value is to large compared to the actual revenue of $233.25


We need to decrease the revenue by 290.25 - 233.25 = 57 dollars.


We'll need to replace some adults with children to bring the revenue down.
Each time we replace 1 adult with 1 child, the revenue drops by $0.75, aka 75 cents, because 2.25 - 1.50 = 0.75


n = number of times we replace 1 adult with 1 child
0.75n = total decrease in revenue
0.75n = 57
n = 57/0.75
n = 76
We'll have 76 instances where we replace 1 adult with 1 child.


The 129 adults drops to 129-76 = 53 adults.
The 0 children increases to 0+76 = 76 children


Check:
53 adults + 76 children = 129 people total
53 adults bring 53*2.25 = $119.25 in revenue
76 children bring 76*1.5 = $114 in revenue
total revenue = 119.25+114 = 233.25
Or as a shortcut we could say: 53*2.25 + 76*1.5 = 233.25
The answers are confirmed.




Summary
<font color=red>53 adults</font>
<font color=red>76 children</font>
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