Question

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 45 quiches 45 quiches 20 quiches 20 quiches 75 quiches

Answer 1

To determine how many quiches the Spanish Club needs to sell to break even, we can set up an equation based on their costs and revenue.

1. Cost to make quiches: The fixed cost is $30, and the variable cost per quiche is $0.50. Therefore, if \( x \) represents the number of quiches, the total cost \( C \) for making \( x \) quiches is given by:

   \[ C = 30 + 0.50x \]

2. Revenue from selling quiches: They will sell each quiche for $2. Thus, the total revenue \( R \) from selling \( x \) quiches is:

   \[ R = 2x \]

3. Break-even condition: They break even when total revenue equals total cost:

   \[ R = C \]

   Substituting the expressions for revenue and cost:

   \[ 2x = 30 + 0.50x \]

4. Solve for \( x \):

   First, we can subtract \( 0.50x \) from both sides:

   \[ 2x - 0.50x = 30 \]

   This simplifies to:

   \[ 1.5x = 30 \]

5. Divide both sides by 1.5:

   \[ x = \frac{30}{1.5} = 20 \]

Thus, the Spanish Club will need to sell 20 quiches to break even. The correct answer is:

20 quiches.