Real-World Systems of Equations Quick Check

Question

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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

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.