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
55
62
16
Let's assume that x represents the number of large cupcakes sold and y represents the number of small cupcakes sold.
From the given information, we can set up the following system of equations:
1.25x + 0.75y = 109.75 (equation 1)
x + y = 105 (equation 2)
We can solve this system of equations using substitution:
From equation 2, we can solve for y in terms of x:
y = 105 - x
Substitute the value of y in equation 1:
1.25x + 0.75(105 - x) = 109.75
Simplify and solve for x:
1.25x + 78.75 - 0.75x = 109.75
0.5x + 78.75 = 109.75
0.5x = 109.75 - 78.75
0.5x = 31
x = 31 / 0.5
x = 62
Therefore, the yearbook club sold 62 large cupcakes.