To determine how many quiches the Spanish Club needs to sell to break even, we need to calculate their total costs and set that equal to their total revenue from selling the quiches.
1. Fixed Costs:
The culinary department charges a fixed fee of $30.
2. Variable Costs:
The cost for ingredients is $0.50 per quiche. If they make \( x \) quiches, the total cost for the ingredients will be \( 0.50x \).
Total Cost Equation:
\[
\text{Total Cost} = 30 + 0.50x
\]
3. Revenue from Sales:
They plan to sell each quiche for $2. If they sell \( x \) quiches, the total revenue will be \( 2x \).
Total Revenue Equation:
\[
\text{Total Revenue} = 2x
\]
4. Break-even Condition:
To break even, the total revenue must equal the total cost:
\[
2x = 30 + 0.50x
\]
5. Solving for \( x \): Subtract \( 0.50x \) from both sides: \[ 2x - 0.50x = 30 \] \[ 1.50x = 30 \]
Now, divide both sides by 1.50: \[ x = \frac{30}{1.50} \] \[ x = 20 \]
Thus, the Spanish Club will need to sell 20 quiches to break even.