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?
A. 75 quiches
B.45 quiches
C.12 quiches
D.20 quiches
To determine how many quiches the Spanish Club needs to sell in order to break even, we can set up an equation.
Let's denote the number of quiches to be sold as 'x'.
The cost of making the quiches is $30 plus $0.50 per quiche for the ingredients. So, the total cost of making 'x' quiches is given by:
Cost = $30 + ($0.50 * x)
The selling price of each quiche is $2. If 'x' quiches are sold, the total revenue from selling 'x' quiches is:
Revenue = $2 * x
In order to break even, the total revenue should be equal to the total cost. Therefore, we can set up the equation:
$2 * x = $30 + ($0.50 * x)
Simplifying the equation:
2x = 30 + 0.50x
Combining like terms:
2x - 0.50x = 30
1.5x = 30
Dividing both sides by 1.5:
x = 30 / 1.5
Simplifying:
x = 20
Therefore, the Spanish Club needs to sell 20 quiches in order to break even.
The answer is D. 20 quiches.
We can set up an equation to solve this problem. Let's call the number of quiches to be sold "x".
The cost to make the quiches is $30 plus $0.50 per quiche, so the total cost is 30 + 0.5x.
The revenue from selling the quiches is $2 per quiche, so the total revenue is 2x.
To break even, the total cost is equal to the total revenue, so we have the equation:
30 + 0.5x = 2x
Subtracting 0.5x and 30 from both sides, we get:
0.5x = 30
Dividing both sides by 0.5, we get:
x = 60
Therefore, they will need to sell 60 quiches to break even.
The correct answer is not given in the options.
To calculate the number of quiches the Spanish Club needs to sell to break even, we need to determine the total cost and the total revenue. Here's how:
1. Calculate the total cost:
The culinary department will make the quiches for $30 plus $0.50 per quiche for the ingredients. Let's say they make "x" quiches. Therefore, the total cost will be:
Total cost = $30 + $0.50x
2. Calculate the total revenue:
The club wants to sell each quiche for $2. Let's say they sell "y" quiches. Therefore, the total revenue will be:
Total revenue = $2y
3. To break even, the total cost must equal the total revenue. So, we can set up an equation:
Total cost = Total revenue
$30 + $0.50x = $2y
4. We know that the total revenue (2y) should be greater than or equal to the total cost ($30 + $0.50x) in order to cover expenses. Let's assume we have to definitively break even, then the total revenue should be equal to the total cost. So we can rewrite the equation as:
$30 + $0.50x = $2y
5. Now, let's find the values of x and y that satisfy this equation:
We know that the cost per quiche is $0.50, and the revenue per quiche is $2. Therefore, to equalize the cost and revenue per quiche, we can ignore the constant term of $30 and divide both sides of the equation by $0.50:
0.50x = 2y
6. Simplify the equation:
x = 4y
7. Now, let's take a look at the answer choices:
A. 75 quiches
B. 45 quiches
C. 12 quiches
D. 20 quiches
8. From the equation x = 4y, we can deduce that the answer should be divisible by 4 to satisfy the equation. Only option C and D satisfy this condition.
9. To break even, the number of quiches sold (y) should be equal to the number of quiches made (x). Since only option D, 20 quiches, satisfies this condition, the answer is:
D. 20 quiches
Therefore, the Spanish Club must sell 20 quiches to break even.