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

75 quiches 75 quiches 45 quiches 45 quiches 12 quiches 12 quiches 20 quiches

Answer 1

To find out how many quiches the Spanish Club needs to sell to break even, we need to determine the total cost and set it equal to the total revenue.

1. Calculate the total cost to make the quiches:

The cost to make quiches consists of a fixed cost of $30 plus a variable cost of $0.50 per quiche. If \( x \) is the number of quiches, the total cost can be expressed as: \[ \text{Total Cost} = 30 + 0.50x \]

2. Calculate the total revenue from selling the quiches:

The Spanish Club wants to sell each quiche for $2. Therefore, the total revenue from selling \( x \) quiches is: \[ \text{Total Revenue} = 2x \]

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

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

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.