Question

unit 2 end of unit recovery points (#3)
ffor this problem (#3), you may complete only the parts that you missed points on in order to receive recovery points on this question on the unit 2 assessment.

1. a jewelry artist is selling necklaces at an art fair. it costs $135 to rent a booth at the fair. the cost of materials for each necklace is $4.50. the artist is selling the necklaces at $12 each.

the inequality $12n>135 + 4.50n$ represents the situation in which the artist makes a profit.
a. will the artist make a profit if she sells 15 necklaces? show how you know.
b. solve for $n$, and then explain what this solution means in context.

Explanation:

Step1: Substitute \(n = 15\) into the inequality

Substitute \(n = 15\) into \(12n\) and \(135+4.50n\).
For \(12n\), we have \(12\times15=180\).
For \(135 + 4.50n\), we have \(135+4.50\times15=135 + 67.5=202.5\).

Step2: Compare the two values

Since \(180>202.5\) is false (\(180<202.5\)), the artist does not make a profit when \(n = 15\).

Step3: Solve the inequality \(12n>135 + 4.50n\)

Subtract \(4.50n\) from both sides:
\(12n-4.50n>135+4.50n - 4.50n\)
\(7.5n>135\)
Divide both sides by \(7.5\):
\(n=\frac{135}{7.5}=18\)

Step4: Interpret the solution

The solution \(n > 18\) means that the artist will make a profit when she sells more than \(18\) necklaces.

Answer:

a. No. When \(n = 15\), \(12\times15=180\) and \(135+4.5\times15 = 202.5\), and \(180<202.5\).
b. \(n>18\). The artist makes a profit when she sells more than \(18\) necklaces.