Avoiding use of "who" while maintaining proper syntax

How do I say the following phrases - typeset in bold - without using "who"? The situation is children on a playground, and attention is given to those on the swings. If I wanted to say something slightly different, the first phrase in bold could be simply stated. "If a child already on the swings were to leave the playground, the fraction of children playing on the swings would be 2/7."

Here is the situation.

There are some children on a playground, and some of them are playing on the swings. If another child were to enter the playground and play on the swings, the fraction of children playing on the swings would be 3/10. If a child already on the playground who had not been playing on the swings were to leave the playground, the fraction of children playing on the swings would be 2/7. Compute the number of children on the playground who are not playing on the swings.

Suggest:

There are some children in a playground, and some of them are playing on the swings. If a new child were to enter the playground and play on the swings, the fraction of children playing on the swings would be 3/10. If a child, already on the playground but not playing on the swings, were to leave the playground, the fraction of children playing on the swings would be 2/7. Compute the number of children that are in the playground but not playing on the swings.

Used the preposition "in the playground", since it is acceptable and on is already used for swings, and no other substitute would work for that phrase.