Question 1203890
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Answers: <font color=red>34 adults, 34 children</font>



Explanation


Consider the hypothetical scenario that all 68 people are adults.


If so, then 68*3.75 = 255 dollars would be the revenue. 
However, the actual money pulled in was $195.50


The gap is 255-195.50 = 59.50
We must reduce the revenue by $59.50 to arrive at the correct revenue.


Each time we replace an adult with a child, the net revenue will go down by $1.75 because 3.75 - 2 = 1.75


n = number of times an adult is replaced by a child
1.75n = decrease in revenue
1.75n = 59.50
n = 59.50/1.75
n = 34


If all 68 people were adults, then we must replace 34 of them with children, so that the revenue drops by $59.50 to arrive at $195.50


68 adults ---> 68-34 = 34 adults
0 children ---> 0+34 = 34 children


There are an equal number of adults and children.


Check:
34 adults + 34 children = 68 people total
34 adults --> 34*($3.75) = $127.50
34 children --> 34*($2) = $68
total money = 127.50+68 = 195.50 dollars
The answers have been confirmed.




Another approach would be to graph the equations
x+y = 68
3.75x+2y = 195.50
to find the point of intersection is (x,y) = (34,34)
Desmos and GeoGebra are two graphing options I recommend.
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