To determine the number of quiches the Spanish club needs to sell in order to break even, we need to calculate the total cost of making the quiches and compare it to the total revenue from selling them.
First, let's calculate the cost per quiche:
Cost per quiche = Cost of ingredients per quiche + Culinary department fee
Cost per quiche = $0.50 + $30 = $30.50
Next, let's calculate the revenue per quiche:
Revenue per quiche = Selling price of each quiche
Revenue per quiche = $2
To break even, the total revenue should be equal to the total cost:
Total revenue = Total cost
Let's assume the number of quiches the Spanish club needs to sell is represented by 'x'.
Total revenue = Revenue per quiche * Number of quiches = $2 * x
Total cost = Cost per quiche * Number of quiches = $30.50 * x
Setting the revenue equal to the cost:
$2 * x = $30.50 * x
Now, let's solve for 'x' to find the number of quiches they need to sell:
Dividing both sides of the equation by x:
$2 = $30.50
Since these two values are not equal, it implies that there is no value of 'x' that satisfies the equation. Thus, the Spanish club cannot break even by selling quiches alone.
To cover their costs, they need to sell more than just quiches. They could consider other fundraising ideas or find additional sources of revenue to cover the cost of the field trip.