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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

20 quiches
20 quiches

45 quiches
45 quiches

75 quiches

1 answer

To find out how many quiches the Spanish Club needs to sell in order to break even, we can set up a simple equation based on the costs and revenue.

  1. Cost to make quiches:

    • Fixed cost: $30
    • Variable cost per quiche: $0.50
    • Total cost for \(x\) quiches: \(30 + 0.50x\)

  2. Revenue from selling quiches:

    • Selling price per quiche: $2
    • Total revenue from selling \(x\) quiches: \(2x\)

  3. Break-even point: To break even, total revenue must equal total costs: \[ 2x = 30 + 0.50x \]

  4. Solving the equation:

    • First, we subtract \(0.50x\) from both sides: \[ 2x - 0.50x = 30 \] \[ 1.5x = 30 \]

    • Next, 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.

So, the correct response is: 20 quiches.