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

45 quiches
45 quiches

20 quiches
20 quiches

12 quiches
12 quiches

75 quiches

Answer 1

To determine how many quiches the Spanish Club needs to sell to break even, we first need to calculate the total cost of making the quiches.

The total cost (C) for making \( x \) quiches can be expressed as: \[ C = 30 + 0.50x \] where \( 30 \) is the fixed cost, and \( 0.50 \) is the cost per quiche.

The revenue (R) from selling \( x \) quiches at $2 each is: \[ R = 2x \]

To break even, we set the total cost equal to the revenue: \[ 30 + 0.50x = 2x \]

Now, let's solve for \( x \):

1. First, subtract \( 0.50x \) from both sides: \[ 30 = 2x - 0.50x \] This simplifies to: \[ 30 = 1.5x \]

2. Next, divide both sides by \( 1.5 \): \[ x = \frac{30}{1.5} \] Calculating this gives: \[ x = 20 \]

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

The correct response is: 20 quiches.