Question

Real-World Systems of Equations Quick Check
4 of 54 of 5 Items
Question
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

75 quiches
75 quiches

12 quiches
12 quiches

45 quiches
45 quiches

20 quiches

Answer 1

To determine how many quiches the Spanish Club needs to sell in order to break even, we can set up an equation based on the costs and revenues.

1. **Calculate the cost to make quiches**:
- Fixed cost: $30
- Variable cost per quiche: $0.50
- Total cost (C) for \( x \) quiches:
\[
C = 30 + 0.50x
\]

2. **Calculate the revenue from selling quiches**:
- Selling price per quiche: $2
- Total revenue (R) for \( x \) quiches:
\[
R = 2x
\]

3. **Set the total cost equal to the total revenue to find breakeven**:
\[
30 + 0.50x = 2x
\]

4. **Solve for \( x \)**:
- Rearranging the equation:
\[
30 = 2x - 0.50x
\]
\[
30 = 1.5x
\]
- Now, divide both sides by 1.5:
\[
x = \frac{30}{1.5} = 20
\]

The Spanish Club needs to sell **20 quiches** to break even.

Therefore, the correct response is:
**20 quiches**.