Let be the volume of the 35% yellow paint the painter will use, and the volume of the 60% yellow paint.
The painter wants to end up with 1 gal of paint, so
Each gallon of 35% yellow paint contributes 0.35 gal of yellow paint, while each gallon of 60% yellow paint contributes 0.60 gal of yellow paint. The painter wants to end up with a 45% mixture, so that