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?

a. 43
b. 55
c. 62***
d. 16

correct. good job.

To solve this problem, we can set up a system of equations based on the given information. Let's denote the number of large cupcakes sold as L, and the number of small cupcakes sold as S.

From the given information, we know that:
L + S = 105 (Eq. 1) (The total number of cupcakes sold is 105)
1.25L + 0.75S = 109.75 (Eq. 2) (The total amount of money raised is $109.75)

We will now solve this system of equations to find the values of L and S.

From Eq. 1, we can rearrange it to solve for L:
L = 105 - S

Substituting this expression for L into Eq. 2:
1.25(105 - S) + 0.75S = 109.75

Expanding and simplifying:
131.25 - 1.25S + 0.75S = 109.75
0.5S = 21.5
S = 43

Now, substitute this value of S back into Eq. 1 to find the value of L:
L + 43 = 105
L = 105 - 43
L = 62

Therefore, the yearbook club sold 62 large cupcakes.

The correct answer is c. 62.