Question

Nasir and Ian decide to open a tutoring business. The two will evenly split the profit from the business. The office costs $300 per month to rent. They charge $30 an hour for their tutoring services. Create an equation to model this situation where x represents number of hours tutoring and y represents total monthly profit.State the domain and range of the equation if they work 20 hours in January, 35 hours in February, 32 hours in March, and 44 hours in April.

Answer 1

Given:

Nasir and Ian decide to open a tutoring business.

Let x represents the number of hours tutoring

and y represents total monthly profit.

The office costs $300 per month to rent.

They charge $30 an hour for their tutoring services.

So, the equation will be:

`y=30x-300`

The domain is the value of x which is the number of hours that can not be negative

they work 20 hours in January, 35 hours in February, 32 hours in March, and 44 hours in April.

So, Domain = [20, 44]

Substitute with the values of x:

When x = 20, y = 30*20 -300 = 600 - 300 = 300

When x = 44, y = 30*44 -300 = 1320 - 300 = 1020

so, the range = [300, 1020]