Question

A jewelry designer sells bead necklaces in a local farmer's market. The profit P that she makes from selling x necklaces is given by P = −x2 + 35x. What is the least number of her necklaces she must sell to make a profit of $300.00?

Answer 1

15

Explanation:

Given that the profit equation from selling x necklaces is

P = −x2 + 35x.

To make a profit of $300, the profit P = 300 then

300 = -x2 + 35x

x2 - 35x + 300 = 0

solve by factorization

x2 - 15x - 20x + 300 = 0

x(x - 15) - 20(x - 15) = 0

(x - 15)(x - 20) = 0

x - 15 = 0 or x - 20 = 0

x = 15 or 20

Since 20 is higher, the least number of her necklaces she must sell to make a profit of $300.00 is 15