Question

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? Select the correct choice.

Answer 1

After substituting n with 15 in the inequality 12n > 135 + 4.50n, the calculation shows that the artist will not make a profit by selling 15 necklaces, as 180 is not greater than 202.50.

Step-by-step explanation:

The question asks whether a jewelry artist will make a profit if she sells 15 necklaces given the inequality 12n > 135 + 4.50n.

This inequality represents the condition for the artist to make a profit, where n is the number of necklaces sold, 12 represents the selling price per necklace, 135 is the fixed cost of renting the booth, and 4.50 is the cost of materials for each necklace.

To determine if the artist makes a profit after selling 15 necklaces, we can substitute n with 15 and calculate:

12 × 15 > 135 + 4.50 × 15
180 > 135 + 67.50
180 > 202.50

As we can see, 180 is not greater than 202.50. Therefore, the artist will not make a profit by selling 15 necklaces.