Roberto plans to start a new job. In preparation, he decides that he should spend no more than 30 hours per week on the job and homework combined. If Roberto wants to have at least 2 homework hours for every 1 hour at his job, what is the maximum number of hours that he should spend at his job each week?

The maximum number of hours that he should spend at his job each week

are 10 hours

Explanation:

First we are going to define the variables

x: Homework's hours

y: Job's hours

How he decides that he should spend no more than 30 hours per week on the job and homework combined and the question is by the maximum number of hours that he should spend at his job, then

x + y = 30

If Roberto wants to have at least 2 homework hours for every 1 hour at his job, then

x = 2y

We solve the system of two equations and two unknowns by equalling

2y = 30 - y

3y = 30

y = 10

The maximum number of hours that he should spend at his job each week

are 10 hours