Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Cooper is starting a business selling handmade necklaces. He has decided to invest an initialamount of $24 for advertising, and materials cost $8 for each necklace he makes. Cooper cansell his creations for $14 per necklace. Once he makes and sells a certain number ofnecklaces, he will break even, with identical expenses and sales. What would the totalexpenses and sales be then? How many necklaces would that take?

Sagot :

Solution:

Given:

For expenses:

[tex]\begin{gathered} Total\text{ expenses}=advertising\text{ fee}+material\text{ cost} \\ Let\text{ the number of necklaces be represented by }x \\ Total\text{ expenses}=24+8x \end{gathered}[/tex]

For sales:

[tex]\begin{gathered} \text{ \$14 per necklace} \\ Total\text{ sales}=14x \end{gathered}[/tex]

At break-even, he will neither make profit nor loss.

At break-even, the expenses are equal to the sales.

Hence,

[tex]\begin{gathered} 24+8x=14x \\ Collecting\text{ the like terms,} \\ 24=14x-8x \\ 24=6x \\ Dividing\text{ both sides by 6 to get }x; \\ \frac{24}{6}=x \\ x=4\text{ necklaces} \end{gathered}[/tex]

Hence,

[tex]\begin{gathered} Total\text{ expenses}=24+8x \\ Total\text{ expenses}=24+8(4) \\ Total\text{ expenses}=24+32 \\ Total\text{ expenses}=\text{ \$56} \\ \\ \\ Total\text{ sales}=14x \\ Total\text{ sales}=14(4) \\ Total\text{ sales}=\text{ \$}56 \end{gathered}[/tex]

Therefore, at break-even, the total expenses will be $56 and the total sales will be $56.

It will take the sales of 4 necklaces to reach break-even.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.