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 year book club sell?
Let's represent the number of large cupcakes as "L" and the number of small cupcakes as "S".
From the problem, we can create two equations:
L + S = 105 (1)
1.25L + 0.75S = 109.75 (2)
To solve this system of equations, let's multiply equation (1) by -0.75:
-0.75L - 0.75S = -78.75 (3)
Adding equations (2) and (3) together, we have:
1.25L + 0.75S -0.75L -0.75S = 31
0.5L = 31
L = 31/0.5
L = <<62=62>>62 large cupcakes.
Thus, the yearbook club sold 62 large cupcakes. Answer: \boxed{62}.