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

20 quiches
20 quiches

12 quiches
12 quiches

75 quiches
75 quiches

45 quiches
45 quiches
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Answer 1

To determine how many quiches the Spanish Club needs to sell in order to break even, we need to calculate the total cost to make the quiches and set it equal to the total revenue from selling them.

1. Cost to make quiches:

   • Fixed cost: $30
   • Variable cost: $0.50 per quiche
   • If they sell \( x \) quiches, the total cost is: \[ \text{Total Cost} = 30 + 0.50x \]

2. Revenue from selling quiches:

   • They sell each quiche for $2, so the total revenue from selling \( x \) quiches is: \[ \text{Total Revenue} = 2x \]

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

4. Solve for \( x \):

   • First, subtract \( 0.50x \) from both sides: \[ 2x - 0.50x = 30 \] \[ 1.5x = 30 \]
   • Now, divide both sides by 1.5: \[ x = \frac{30}{1.5} = 20 \]

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