Aproblem states: "there are 9 more children than parents in a room. there are 25 people in the room in all. how many children are there in the room? "

let c represent the number of children.

which expression represents the number of parents?

Let c = number of children in the room.
Let p = the number of parents in the room.

There are 9 more children than parents in the room. Therefore
c = p +9           (1)

There are 25 people in the room. Therefore
c + p = 25        (2)

The expression for the number of parents is 
p = 25 -c


Note:
We can determine the number of children and parents.
Substitute (1) into (2).
p + 9 + p = 25
2p + 9 = 25
2p = 25 - 9 = 16
p = 16/2 = 8
c = p + 9 = 8 + 9 = 17

Number of children = 17
Number of parents  = 8