Let the number of pies (and cakes) Fadi sold be \( x \).
Profit from pies:
- Expense per pie = $5
- Total expense for pies = \( 5x \)
- Total profit from pies = $250
Thus, the total revenue from the pies can be expressed as: \[ \text{Revenue from pies} = \text{Total expense} + \text{Total profit} = 5x + 250 \]
Profit from cakes:
- Expense per cake = $4
- Total expense for cakes = \( 4x \)
- Total profit from cakes = $200
Thus, the total revenue from cakes can be expressed as: \[ \text{Revenue from cakes} = \text{Total expense} + \text{Total profit} = 4x + 200 \]
Since Fadi earned the same total profit for pies and cakes, we can equate the profits: \[ 250 = 200 \]
Actually, as per the question, we are meant to analyze the conditions where total expenses differ while keeping the profits balanced.
Total costs (expenses) of pies and cakes can also be set according to the same quantities sold: For pies: Total revenue from pies = (Selling Price per pie * x) - (5 * x) For cakes: Total revenue from cakes = (Selling Price per cake * x) - (4 * x)
Since the profits are already given, we can compare these.
Next, calculate the quantities directly, using just the profit values since they are driven resulted instead by the scenarios they represent.
Given: Profit from pies: $250 Profit from cakes: $200
To equalize, it would show that we need to find \( x \) such that: \[ 5x + 250 = 4x + 200 \]
\[ 5x + 250 - 4x = 200 \]
This results in: \[ x + 250 = 200 \] \[ x = 200 - 250 \] Thus, This does not yield the sold quantities context.
However, considering how the profits differ from pie to cake as sold quantity impacting on profit outputs:
- If \( x = 50 \): Profit left as \( 50(5)=250\)
- if \( x = 40\): Profit yields \( 40(4)=200\) Comes that set balance given.
Giving us the option matched: Thus Option A (50 pies) would yield where profit values set to be analysis clear against \( x=40\). Therefore, selling 50 pies yields the situation.