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Sandra makes and sells bracelets. It costs her [tex]$\$[/tex] 2[tex]$ to make each bracelet, plus a one-time cost of $[/tex]\[tex]$ 15$[/tex] for supplies. She plans to sell each bracelet for [tex]$\$[/tex] 5[tex]$. Let $[/tex]x$ represent the number of bracelets.

Which equation can be used to find the number of bracelets she needs to sell to break even?

A. [tex]$2x - 5x = 15$[/tex]

B. [tex]$2x + 5x = 15$[/tex]

C. [tex]$2x + 15 = 5x$[/tex]

D. [tex]$5x + 15 = 2x$[/tex]



Answer :

GinnyAnswer
To determine which equation Sandra can use to find the number of bracelets she needs to sell to break even, we need to establish both her cost and her revenue.

1. Total Cost:
- It costs $2 to make each bracelet.
- There is an additional one-time cost of $15 for supplies.

Therefore, the total cost \(C\) can be represented as:
[tex]\[ C = 2x + 15 \][/tex]
where \(x\) is the number of bracelets.

2. Total Revenue:
- She plans to sell each bracelet for $5.

Therefore, the total revenue \(R\) can be represented as:
[tex]\[ R = 5x \][/tex]

3. Break-Even Point:
To find the break-even point, we need the total cost to equal the total revenue:
[tex]\[ \text{Total Cost} = \text{Total Revenue} \][/tex]

Substituting these expressions, we get:
[tex]\[ 2x + 15 = 5x \][/tex]

Rewriting this to match the provided options, the correct equation that represents the break-even point is:
[tex]\[ 2x + 15 = 5x \][/tex]

Hence, the equation Sandra can use to find the number of bracelets she needs to sell to break even is:
[tex]\[ 2x + 15 = 5x \][/tex]

Therefore, the correct answer choice is:
[tex]\[ \boxed{2x + 15 = 5x} \][/tex]

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