the spanish club at santa fe middle school wants to sell 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
To determine how many quiches the Spanish club needs to sell in order to break even, we'll calculate the break-even point by considering the costs and the revenue.
Cost per quiche:
Culinary department cost: $30
Cost of ingredients per quiche: $0.50
Total cost per quiche: $30 + $0.50 = $30.50
Revenue per quiche: $2
Let's assume the number of quiches they need to sell to break even is "x."
Total cost = Total revenue
$30.50 * x = $2 * x
Now, we can solve for x:
30.50x = 2x
30.50x - 2x = 0
28.50x = 0
x = 0/28.50
x = 0
According to the calculations, in order to break even, the Spanish club would need to sell 0 quiches. However, this doesn't make sense as the club needs to sell some quiches to cover their costs. It's likely that there was an error in the given information or the calculations.
To break even, the Spanish club needs to cover the cost of making the quiches, which is $30 for the culinary department and $0.50 per quiche for the ingredients. Let's call the number of quiches they need to sell to break even x.
The cost of making the quiches is a fixed cost of $30, regardless of the number of quiches made.
The cost of the ingredients per quiche is $0.50. So, the total cost of the ingredients for x quiches is 0.5x.
The total cost of making the quiches is the sum of the fixed cost and the cost of the ingredients:
Total cost = Fixed cost + Cost of ingredients
Total cost = $30 + $0.5x
The revenue from selling x quiches at $2 per quiche is:
Revenue = Price per quiche x Number of quiches sold
Revenue = $2x
For the Spanish club to break even, the total cost of making the quiches must equal the revenue from selling the quiches:
$30 + $0.5x = $2x
To solve for x, let's isolate x on one side of the equation:
$0.5x - $2x = -$30
-$1.5x = -$30
Now, divide both sides of the equation by -1.5:
x = -$30 / -$1.5
x = 20
Therefore, the Spanish club will need to sell 20 quiches in order to break even.
To determine how many quiches the Spanish club at Santa Fe Middle School needs to sell in order to break even, we'll need to calculate the total cost and the total revenue.
Let's break down the cost and revenue components:
Cost:
- The culinary department charges $30 to make the quiches.
- Additionally, the cost of ingredients per quiche is $0.50.
Revenue:
- The Spanish club plans to sell each quiche for $2.
To break even, the total cost should equal the total revenue. Mathematically, we can express this as:
Total cost = Total revenue
Let's calculate the total cost first:
- The cost for making the quiches is a fixed $30.
- The cost for the ingredients is $0.50 per quiche.
- Therefore, the total cost can be calculated as: Total cost = $30 + ($0.50 * number of quiches)
Next, let's calculate the total revenue:
- The Spanish club plans to sell each quiche for $2.
- The total revenue can be calculated as: Total revenue = $2 * number of quiches
Since the total cost should equal the total revenue to break even, we can set up the equation:
$30 + ($0.50 * number of quiches) = $2 * number of quiches
Now, we need to solve this equation for the number of quiches.
1. Start by isolating the number of quiches by moving all terms involving the number of quiches to one side:
$30 = $2 * number of quiches - ($0.50 * number of quiches)
2. Simplify the equation:
$30 = $1.50 * number of quiches
3. Divide both sides by $1.50 to solve for the number of quiches:
($30 / $1.50) = number of quiches
4. Evaluate the expression:
20 = number of quiches
Therefore, the Spanish club at Santa Fe Middle School needs to sell 20 quiches in order to break even.