The Spanish Club at Santa Fe Middle School wants to sell mini quiches to raise money for a field trip. The culinary department at their school will make the quiches for $30 plus $0.50 per quiche for the ingredients. The Spanish Club wants to sell each quiche for $2. How many quiches will they need to sell in order to break even?(1 point) Responses 12 quiches 12 quiches 20 quiches 20 quiches 45 quiches 45 quiches 75 quiches 75 quiches

Answer 1

To determine how many quiches the Spanish Club needs to sell to break even, we first need to calculate their total costs and their total revenue from selling the quiches.

Step 1: Calculate Total Costs

The cost to make the quiches consists of a fixed cost and a variable cost per quiche:

• Fixed cost: $30
• Variable cost per quiche: $0.50

If they sell \( x \) quiches, the total cost \( C \) can be calculated as: \[ C = 30 + 0.50x \]

Step 2: Calculate Total Revenue

The revenue from selling the quiches can be calculated as: \[ R = 2x \] (since they sell each quiche for $2).

Step 3: Set Up the Break-Even Equation

To break even, the total revenue must equal the total costs: \[ 2x = 30 + 0.50x \]

Step 4: Solve the Equation

Now, we solve for \( x \):

1. Subtract \( 0.50x \) from both sides: \[ 2x - 0.50x = 30 \] \[ 1.5x = 30 \]

2. Now, divide by \( 1.5 \): \[ x = \frac{30}{1.5} = 20 \]

Conclusion

The Spanish Club needs to sell 20 quiches to break even.

So the answer is: 20 quiches