Question

a jewelry artist is selling necklaces at an art 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. Write an inequality to show the number of necklaces, n, the artist must sell to make a profit. Show your reasoning.

Answer 1

a. The artist will not make a profit when selling 15 necklaces. b. The artist must sell more than 18 necklaces to make a profit.

Step-by-step explanation:

a. To determine if the artist will make a profit when selling 15 necklaces, we can substitute the value of n as 15 into the inequality and check if it is true.
12n > 135 + 4.50n
12(15) > 135 + 4.50(15)
180 > 135 + 67.50
180 > 202.50
Since 180 is not greater than 202.50, the artist will not make a profit when selling 15 necklaces.

b. To determine the number of necklaces the artist must sell to make a profit, we can set up the inequality equation as follows:
12n > 135 + 4.50n
Simplifying the equation, we get
7.50n > 135
Dividing both sides by 7.50, we get
n > 18
Therefore, the artist must sell more than 18 necklaces to make a profit.