Answer: 338 children
Explanation:
Assume the children are represented by x and the adults are y.
Relevant equations will be:
x + y = 507 people
1.75x + 2.25y = 971.75
y = 507 - x
1.75x + 2.25 * ( 507 - x) = 971.75
1.75x + 1,140.75 - 2.25x = 971.75
1.75x - 2.25x = 971.75 - 1,140.75
-0.5x = -169
x = -169/-0.5
x = 338 children
Adults = 507 - 338
= 169 adults