Diego works at a scooter dealership that sells two scooter models: a $5,000 standard model and a $7,000 racing model. Last month, his goal was to sell at least 36 scooters. If Diego met his goal and brought in over $250,000 in sales, write a system of inequalities that describes the possible number of standard model scooters and the possible number of racing model scooters that Diego sold last month.

Let $ x $ be the number of standard model scooters sold.
Let $ y $ be the number of racing model scooters sold.

The system of inequalities is:

\[ x + y \geq 36 \]
\[ 5000x + 7000y > 250000 \]

Diego's sales can be articulated as a system of inequalities where x is the number of standard model scooters and y is the number of racing model scooters. The inequalities are x + y ≥ 36 and 5000x + 7000y > 250,000, representing the goal of at least 36 scooters sold and the total sales being over $250,000.

Explanation:

To create a system of inequalities for the scenario where Diego is selling scooters, we need to define our variables first. Let's say x is the number of standard model scooters sold and y is the number of racing model scooters sold. According to the problem, Diego's goal was to sell at least 36 scooters and brought in over $250,000 in sales. This can be translated into two inequalities:

The total number of scooters sold should be at least 36: x + y ≥ 36.
The total sales amount for the scooters should exceed $250,000. Given the standard scooter costs $5,000 and the racing model costs $7,000, the inequality is 5000x + 7000y > 250,000.

So, the system of inequalities to describe the number of each model sold by Diego last month is:

x + y ≥ 36
5000x + 7000y > 250,000

To find the possible values for x and y, you would graph these inequalities in the coordinate plane and look for the region where they both are satisfied.