The yearbook club is having a bake sale to raise money for the senior class. Large cupcakes are sold for $1.25 each and small cupcakes are sold for $0.75 each. if 105 cupcakes were sold for a total amount of $109.75, how many large cupcakes did the yearbook club sell?
Let's assume that the number of large cupcakes sold is x.
Then the number of small cupcakes sold is (105 - x).
The total amount of money earned from selling the large cupcakes is x * $1.25.
The total amount of money earned from selling the small cupcakes is (105 - x) * $0.75.
The total amount of money earned from selling all the cupcakes is x * $1.25 + (105 - x) * $0.75.
Therefore, according to the problem, we have the equation: x * $1.25 + (105 - x) * $0.75 = $109.75.
Simplifying 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 of the equation, we get: 0.5x = 31.
Dividing both sides of the equation by 0.5, we get: x = 62.
Therefore, the yearbook club sold 62 large cupcakes. Answer: \boxed{62}.