Question 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 16
Let's assume that the number of large cupcakes sold is x and the number of small cupcakes sold is y.
According to the given information, the total number of cupcakes sold is 105, so we can write the equation x + y = 105.
The price of a large cupcake is $1.25 and the price of a small cupcake is $0.75. The total amount earned from selling the cupcakes is $109.75, so we can write the equation 1.25x + 0.75y = 109.75.
Now we can solve these two equations to find the values of x and y.
First, we can multiply the first equation by -0.75 to eliminate the y variable.
-0.75(x + y) = -0.75(105)
-0.75x - 0.75y = -78.75
Next, we can add this equation to the second equation:
(-0.75x - 0.75y) + (1.25x + 0.75y) = -78.75 + 109.75
0.5x = 31
x = 31 / 0.5
x = 62
Therefore, the yearbook club sold 62 large cupcakes.