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 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}.