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)
Responses
43
43
55
55
62
62
16
Let's represent the number of large cupcakes sold as L and the number of small cupcakes sold as S.
From the problem, we know two things:
1. There were a total of 105 cupcakes sold: L + S = 105
2. The total amount raised was $109.75: 1.25L + 0.75S = 109.75
We can solve these two equations simultaneously to find the values of L and S.
From the first equation, we can solve for L: L = 105 - S
Substituting this value of L into the second equation, we have:
1.25(105 - S) + 0.75S = 109.75
131.25 - 1.25S + 0.75S = 109.75
-0.5S = -21.5
S = -21.5 / -0.5
S = 43
So, the number of small cupcakes sold was 43.
Substituting this value of S into the first equation, we can solve for L:
L + 43 = 105
L = 105 - 43
L = 62
So, the number of large cupcakes sold was 62.
Therefore, the answer is 62 large cupcakes were sold by the yearbook club.