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Let x be the number of large cupcakes sold.
The total amount from selling large cupcakes is 1.25x.
The total amount from selling small cupcakes is 0.75(105 - x).
The total amount from selling all cupcakes is 1.25x + 0.75(105 - x), which is equal to $109.75.
Expanding the equation we get 1.25x + 78.75 - 0.75x = 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.
Therefore, the yearbook club sold 62 large cupcakes. Answer: 62.