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

first one : 7.5x -100 > 79.86 + 5.8x

second one : x > 105.8

last one : 106

Explanation:

Answer 2

106 items

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.