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A jewelry artist is selling necklaces at an art fair. It costs $155 to rent a booth at the fair. The cost of materials for each necklace is $5.50. The artist is selling the necklaces at $14 each. The inequality 14𝑛 155 + 5.50𝑛 represents the situation in which the artist makes a profit.

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Anonymous
0


a. Will the artist make a profit if she sells 16 necklaces? Show how you know.

b. Write an inequality to show the number of necklaces, 𝑛, the artist must sell to make a profit. Show your reasoning

Sahil Khan
0

a.

It is given that is costs $155 to rent a booth, and that the cost of each necklace is $5.50.  Assuming that the artist sells 20 necklaces, we substitute n = 16 in the inequality to get

14 \cdot 16 \gt 155 + 5.50 \cdot 16  

244 \gt 155 + 88

224 \ngtr 243


So, the artist does not make a profit when she sells 20 necklaces, since substituting n = 16, does not satisfy the given inequality.


b.

Solve the given inequality 14 n \gt 155 + 5.50 n  for n.

14 n - 5.50 n \gt 155

8.50 n \gt 155

n \gt \frac{155}{8.50} = 18.235 .

Rounding it off to a whole number because the number of necklaces cannot be a decimal number, the artist must sell at least 19 necklaces to make a profit.