Question

An enterpreneur is selling necklaces at an art fair. It costs $143 to rent a booth at the fair. The cost of the materials for each necklace is 5.50. The enterpreneur is selling the necklaces at $10 each. The inequality 10n > 143 + 5.50n represents the situation in which the enterpreneur makes a profit. (a) Will the entrepreneur make a profit if she sells 15 necklaces? (b) Show how you know. (c) Write an inequality to show the number of necklaces, n. the enterpreneur must sell to make a profit. (d) Show your reasoning.

Answer 1

(a), (b) 10(15) > 143 + 5.50(15)

150 > 143 + 82.50

150 > 225.50 (false)

The entrepreneur does not make a

profit.

(c), (d) 10n > 143 + 5.50n

4.50n > 143

n ≥ 32 necklaces