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Let x be the number of large cupcakes sold
The number of small cupcakes sold was 105 - x
The total price of large cupcakes is x * $1.25
The total price of small cupcakes is (105 - x) * $0.75
The total price was x * $1.25 + (105 - x) * $0.75 = $109.75
Multiplying through the parentheses, we get x * $1.25 + $78.75 - x * $0.75 = $109.75
Combining like terms, we get $0.5x + $78.75 = $109.75
Subtracting $78.75 from both sides, we get $0.5x = $31
Dividing both sides by $0.5, we get x = 62 large cupcakes. Answer: \boxed{62}.