Final answer:
George Gershwin's composition that provided a steady income for a decade was 'Rhapsody in Blue'
Step-by-step explanation:
George Gershwin's composition that gave him a steady source of income for a decade was 'Rhapsody in Blue'. This piece, written in 1924, is a blend of classical music and jazz and became one of Gershwin's most famous works. It was commissioned by a band leader named Paul Whiteman for a concert called 'An Experiment in Modern Music' and became an instant success, earning Gershwin royalties and establishing his reputation as a composer.