This is actually how PGP/GPG operates.
When you encrypt something to a public key, it first encrypts the data with a symmetric key. Then it encrypts the symmetric key with public key cryptography, and appends it to the encrypted data.
Assymmetric encryption is not suitable for big amounts of data, due to speed of encryption. Thus this improves speed of encryption.
In addition, it allows for multiple recipients of the data without significant increase in size; only the symmetric key has to be encrypted for each recipient, while the bulk data can be included only once.