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?
43
55
62
16
Let's say the number of large cupcakes sold is L and the number of small cupcakes sold is S.
From the problem, we know that:
1) L + S = 105 (the total number of cupcakes sold)
2) 1.25L + 0.75S = 109.75 (the total amount earned from cupcake sales)
We can solve these equations simultaneously to find the values of L and S.
First, we can solve equation 1) for either L or S.
L = 105 - S
Now we can substitute this value for L in equation 2):
1.25(105 - S) + 0.75S = 109.75
Distribute 1.25:
131.25 - 1.25S + 0.75S = 109.75
Combine like terms:
-0.5S = -21.5
Divide by -0.5:
S = 43
Now we can substitute this value for S in equation 1):
L + 43 = 105
Subtract 43 from both sides:
L = 62
So, the yearbook club sold 62 large cupcakes. The answer is 62.