Answer: 219 children and 72 adults swam at the public pool that day.
Explanation:
Let x = Number of children , y= Number of adults.
As per given, x+y = 291 (i)
1.5x+2y = 472.50 (ii)
Multiply 2 on both sides of (i) , we get
2x+2y = 582 (iii)
Eliminate (ii) from (iii), we get
0.5x = 109.5

Put value of x= 219 in (i)
219+y= 291
⇒ y = 291-219 = 72
Hence, 219 children and 72 adults swam at the public pool that day.