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

45 quiches
45 quiches

12 quiches
12 quiches

75 quiches

Answer 1

To find out how many mini quiches the Spanish Club needs to sell in order to break even, we can set up an equation.

First, let's determine the total cost (TC) for the culinary department to make the quiches. The total cost can be calculated as follows:

TC = Fixed Cost + Variable Cost per quiche × Number of quiches TC = $30 + $0.50 × \( x \) (where \( x \) is the number of quiches)

The selling price (SP) per quiche is $2, so the total revenue (TR) from selling \( x \) quiches is:

TR = Selling Price per quiche × Number of quiches TR = $2 × \( x \)

To break even, the total revenue must equal the total cost:

TR = TC $2 × \( x \) = $30 + $0.50 × \( x \)

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

\[ 2x = 30 + 0.5x \]

Subtract \( 0.5x \) from both sides:

\[ 2x - 0.5x = 30 \]

This simplifies to:

\[ 1.5x = 30 \]

Now, divide both sides by 1.5:

\[ x = \frac{30}{1.5} \] \[ x = 20 \]

The Spanish Club needs to sell 20 quiches in order to break even.

Therefore, the correct response is 20 quiches.