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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

20 quiches
20 quiches

12 quiches
12 quiches

75 quiches
75 quiches

45 quiches

1 answer

To find out how many quiches the Spanish Club needs to sell in order to break even, we first need to set up the equation for their total costs and total revenue.

Total Costs:

The total cost (C) of making the quiches consists of a fixed cost and a variable cost per quiche:

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

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

Total Revenue:

The total revenue (R) from selling quiches, if each quiche is sold for $2, is: \[ R = 2x \]

Break-Even Point:

The break-even point occurs when total costs equal total revenue: \[ 30 + 0.50x = 2x \]

Solving for \( x \):

  1. Rearranging the equation: \[ 30 = 2x - 0.50x \] \[ 30 = 1.5x \]

  2. Dividing both sides by 1.5: \[ x = \frac{30}{1.5} \] \[ x = 20 \]

Therefore, they need to sell 20 quiches in order to break even.

The correct response is: 20 quiches