The admission fee for a charity event is 7 dollars for children and 10 dollars for adults the event was attended by 700 people and the total amount collected in admissions was 6,400 dollars

Given:
$7/child
$10/adult
Total people = 700
Total money = $6,400

First, make two equations.
Let a = # of adults & Let c = # of children.
Let p = total people

1.      a+c = 700
2.  10a+7c = 6,400

Then, rearrange the equation to solve for a variable.
c = 700-a

Substitute (700-a) for c, or the # of children in the second equation.
10a+(700-a) = 6400
9a+700 = 6400
9a+700-700 = 6400-700
9a = 5700
9a/9 = 5700/9 
a = 633  = # of adults attended

700-633 = c = 66  = # of children attended