Question

A photographer needs $4000 to purchase a printer for her new business. Each photo she prints costs an additional $3.56. She plans to sell each photo for $9.99. Which of the following expressions represents the profit P(x) the photographer will make for each photo x that she sells?

a) P(x) = 6.43x + 4000
b) P(x) = 6.43x - 4000
c) P(x) = 13.55x + 4000
d) P(x) = 13.55x - 4000

Answer 1

The profit P(x) the photographer will make for each photo x that she sells can be represented by the expression P(x) = 13.55x - 4000, as she earns $6.43 per photo sold after deducting the printing cost. The option d) P(x) = 13.55x - 4000 is the correct expression.

Step-by-step explanation:

The profit P(x) the photographer will make for each photo x that she sells can be represented by the expression P(x) = 13.55x - 4000.

To calculate the profit, we subtract the cost of printing each photo, which is $3.56, from the selling price of each photo, which is $9.99. So, the profit per photo is $9.99 - $3.56 = $6.43. Therefore, the expression that represents the profit for each photo sold is P(x) = 6.43x.

Since the photographer needs to first recover the cost of the printer, we subtract $4000 from the profit expression, resulting in P(x) = 6.43x - 4000. Therefore, option d) P(x) = 13.55x - 4000 represents the profit the photographer will make for each photo sold.