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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.
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