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 assume the number of large cupcakes sold is x.
The number of small cupcakes sold would be 105 - x.
The total amount of money raised from selling large cupcakes would be 1.25 * x.
The total amount of money raised from selling small cupcakes would be 0.75 * (105 - x).
The sum of these two amounts should equal $109.75, so we can write the equation:
1.25 * x + 0.75 * (105 - x) = 109.75
Simplifying the equation:
1.25x + 0.75 * 105 - 0.75x = 109.75
1.25x + 78.75 - 0.75x = 109.75
0.5x = 109.75 - 78.75
0.5x = 31
x = 31 / 0.5
x = 62
The yearbook club sold 62 large cupcakes.
Let's assume the number of large cupcakes sold as 'L' and the number of small cupcakes sold as 'S'.
We know that the price of each large cupcake is $1.25 and the price of each small cupcake is $0.75.
From the given information, we have two equations:
1. L + S = 105 (Equation 1, because the total number of cupcakes sold is 105)
2. 1.25L + 0.75S = 109.75 (Equation 2, because the total amount earned is $109.75)
Now, we need to solve these equations to find the value of L.
We can use substitution or elimination method to solve these equations.
Let's use the elimination method:
From Equation 1, we have L = 105 - S
Substituting this value in Equation 2, we get:
1.25(105 - S) + 0.75S = 109.75
Distributing 1.25 to 105 and -1.25 to -S, we get:
131.25 - 1.25S + 0.75S = 109.75
Combining like terms, we have:
0.5S = 109.75 - 131.25
0.5S = -21.5
Dividing both sides by 0.5, we get:
S = -21.5 / 0.5
S = 43
So, the number of small cupcakes sold is 43.
Now, substituting this value back into Equation 1, we get:
L + 43 = 105
Subtracting 43 from both sides, we get:
L = 105 - 43
L = 62
Therefore, the yearbook club sold 62 large cupcakes.
To solve this problem, we need to set up a system of equations. Let's define two variables: "L" for the number of large cupcakes and "S" for the number of small cupcakes.
Based on the information given, we can form two equations:
1. L + S = 105 (total number of cupcakes sold)
2. 1.25L + 0.75S = 109.75 (total amount earned from cupcake sales)
Now we can solve these two equations simultaneously to find the values of L and S.
We can use the substitution method to solve this system of equations. Let's solve equation 1 for S:
S = 105 - L
Now substitute this value of S in equation 2:
1.25L + 0.75(105 - L) = 109.75
Simplify the equation:
1.25L + 78.75 - 0.75L = 109.75
Combine like terms:
(1.25L - 0.75L) + 78.75 = 109.75
0.50L + 78.75 = 109.75
Subtract 78.75 from both sides:
0.50L = 31
Divide both sides by 0.50:
L = 62
Therefore, the yearbook club sold 62 large cupcakes.