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Candy sells cupcakes. She makes \[tex]$2 on each cupcake she sells. Each month, she spends \$[/tex]346 on supplies. Which of the following represents a break-even equation?

A. [tex]0 = 2x - 346[/tex]
B. [tex]y = 2x - 346[/tex]
C. [tex]376 = -2x[/tex]
D. [tex]y = 2x + 346[/tex]


Sagot :

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]
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