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?
(1 point)
43
55
62
16
Let's represent the number of large cupcakes as L and the number of small cupcakes as S.
We can set up a system of equations based on the given information:
L + S = 105 (equation 1)
1.25L + 0.75S = 109.75 (equation 2)
To solve this system, we can use substitution or elimination.
Let's solve it using substitution:
From equation 1, we can express S in terms of L: S = 105 - L
Substituting this expression into equation 2, we get:
1.25L + 0.75(105 - L) = 109.75
1.25L + 78.75 - 0.75L = 109.75
0.5L + 78.75 = 109.75
0.5L = 109.75 - 78.75
0.5L = 31
L = 31 / 0.5
L = 62
So the yearbook club sold 62 large cupcakes.
Therefore, the correct answer is 62.