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Sheila’s car goes 150/5 = <<150/5=30>>30 miles per gallon of gas.
Derek’s car goes 105/3 = <<105/3=35>>35 miles per gallon of gas.
Derek’s car goes 35 - 30 = <<35-30=5>>5 more miles per gallon of gas than Sheila’s car. Answer: \boxed{5}.