Question

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Real-World Systems of Equations Quick Check
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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

12 quiches
12 quiches

45 quiches
45 quiches

75 quiches
75 quiches

20 quiches

Answer 1

To determine the number of quiches the Spanish Club needs to sell in order to break even, we can set up an equation.

Let \( x \) be the number of quiches sold.

The total cost of making the quiches is given by:
\[ \text{Total Cost} = 30 + 0.50x \]

The revenue from selling the quiches is:
\[ \text{Total Revenue} = 2x \]

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

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

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

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

The Spanish Club needs to sell **20 quiches** to break even. The correct response is:

**20 quiches**