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?
The inequality that will determine the number of items that need to be sold to make a profit is 7.5x-100> 79.86 + 5.8x

The solution to the inequality is: X>11.85 X<105.8 X>105.8

The inequality that will determine the number of items that need to be sold to make a profit is: 12 100 106

Answer 1

1. 7.5x - 100 > 79.86 + 5.8x

2. x > 105.8

3. 106

Answer 2

Revenues > costs
7.5x – 100 > 79.86 + 5.8x

7.5x - 5.8x > 79.86 + 100

1.7x > 179.86

x > 179.86 / 1.7

x > 105.8

Then, the minimum number of objects that need to be sold is 106 (the smallest integer greater than 105.8)