Certainly! Let's break down the problem step by step.
Given:
- Candy makes \[tex]$2 on each cupcake she sells.
- Each month, Candy spends \$[/tex]346 on supplies.
We need to determine which equation represents the break-even point for Candy.
Step 1: Understand the break-even point
The break-even point occurs when Candy's profit is zero. This means her total revenue from selling cupcakes is equal to her total expenses.
Step 2: Define the variables
Let [tex]\( x \)[/tex] be the number of cupcakes Candy sells in a month.
Let [tex]\( y \)[/tex] be the profit for Candy.
Step 3: Express revenue and expenses
Revenue:
- Since Candy makes \[tex]$2 on each cupcake, her revenue from selling \( x \) cupcakes is \( 2x \).
Expenses:
- Her fixed monthly expense is \$[/tex]346.
Step 4: Set up the profit equation
Profit ([tex]\( y \)[/tex]) is the difference between revenue and expenses:
[tex]\[ y = \text{Revenue} - \text{Expenses} \][/tex]
[tex]\[ y = 2x - 346 \][/tex]
Step 5: Identify the break-even equation
At the break-even point, Candy's profit ([tex]\( y \)[/tex]) is 0:
[tex]\[ 0 = 2x - 346 \][/tex]
Now, examine the given options:
1. [tex]\( 0 = 2x - 346 \)[/tex]
2. [tex]\( y = 2x - 346 \)[/tex]
3. [tex]\( 376 = -2x \)[/tex]
4. [tex]\( y = 2x + 346 \)[/tex]
The correct option representing the break-even equation, where profit ([tex]\( y \)[/tex]) equals zero, is:
[tex]\[ 0 = 2x - 346 \][/tex]
So, the correct answer is:
[tex]\[ 0 = 2x - 346 \][/tex]
