Alternatively, if you do not want to deal with 2 variables, make the ratio of the girls equal in the before and after situations, then you can write an equation for the change in the ratio for the adults using u.

Before:

      B              G                 A

      4            3(x2)           1 (x2)

? left       no change       +21 (x2)

After:

      B              G                 A

      1             2(x3)            3 (x3)

2u + 42 = 9u

=> 7u = 42          Children at the pool/party at the beginning is 4u+3u=7u =42

This question is very poorly worded.  It should just keep to the birthday party throughout instead of changing it to swimming pool half way.  Not all kids have attended a birthday party at the poolside to see the link.  Kindly feedback to the teacher.

Before:

      B              G                 A

      4u            3u                u

? left       no change       +21

After:

      B              G                 A

      p             2p                3p

3u=2p => p =(3/2)u

u+21 = 3p

u+21 = 3(3/2)u = (9/2)u

2u + 42 = 9u

=> 7u = 42          Children at the pool/party at the beginning is 4u+3u=7u =42