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)

Question

Responses

12 quiches
12 quiches

75 quiches
75 quiches

45 quiches
45 quiches

20 quiches

Answer 1

To find the break-even point, we need to determine the total cost of making the quiches and set that equal to the total revenue from selling the quiches.

1. Cost to make the quiches:

   • Fixed cost: $30 (this is a one-time fee)
   • Variable cost per quiche: $0.50
   • If \( q \) is the number of quiches, the total cost \( C \) is: \[ C = 30 + 0.50q \]

2. Revenue from selling quiches:

   • Selling price per quiche: $2
   • Total revenue \( R \) from selling \( q \) quiches is: \[ R = 2q \]

3. Setting the total cost equal to the total revenue to find the break-even point: \[ 30 + 0.50q = 2q \]

4. Rearranging the equation: \[ 30 = 2q - 0.50q \] \[ 30 = 1.5q \]

5. Solving for \( q \): \[ q = \frac{30}{1.5} = 20 \]

Therefore, the Spanish Club needs to sell 20 quiches to break even.

Final Answer: 20 quiches