Question

To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit?

Answer 1

Answer:

106 items

Step-by-step explanation:

We are actually finding the "break even" point, where revenue = costs.

Set the revenue 7.5x - 100 equal to the costs 79.86 + 5.8x:

7.5x - 100 = 79.86 + 5.8x

Group the x terms together:    

1.7x  - 100  =  79.86

and then group the constants together on the right side:

  1.7x = 179.86

Solving for x, we get 105.8 (items)

Round this up:  106 items

The company will begin making a profit as production passes 106 items.