Questions: A bake sale committee would like to determine how many cupcakes they need to sell in order to break even. The location for their bake sale will cost 100. Every dozen cupcakes costs 9 to make. Every cupcake will be sold for 1.00. How many cupcakes will the committee need to sell in order to break even? Round your answer to the next largest whole number.

Solution Steps

To determine how many cupcakes the committee needs to sell to break even, we need to calculate the total cost and the total revenue. The total cost includes the location cost and the cost of making the cupcakes. The total revenue is the number of cupcakes sold multiplied by the selling price per cupcake. We then solve for the number of cupcakes where the total revenue equals the total cost.

The total cost \( C \) for the bake sale committee consists of the location cost and the cost of making the cupcakes. The location cost is given as:

\[ C_{\text{location}} = 100 \]

The cost to make cupcakes is calculated based on the cost per dozen:

\[ C_{\text{dozen}} = 9 \quad \Rightarrow \quad C_{\text{cupcake}} = \frac{C_{\text{dozen}}}{12} = \frac{9}{12} = 0.75 \]

The total revenue \( R \) from selling \( x \) cupcakes at a price of \( 1.00 \) per cupcake is:

\[ R = 1.00 \cdot x \]

To break even, the total cost must equal the total revenue:

\[ C_{\text{location}} + C_{\text{cupcake}} \cdot x = R \]

Substituting the known values:

\[ 100 + 0.75x = 1.00x \]

Rearranging the equation gives:

\[ 100 = 1.00x - 0.75x \]

This simplifies to:

\[ 100 = 0.25x \]

Solving for \( x \):

\[ x = \frac{100}{0.25} = 400 \]

Final Answer