Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekends. one week ramiro earned a total of $650. he worked 5 times as many hours during the week as he did on the weekend. write and solve a system of equations to determined how many hours of overtime ramiro worked on the weekend.

Two key parts of this solution. 

1) Set up the right equations. Let's say that x is the number of hours during the weekdays, and y is the number of weekend hours. In each week, Ramiro will earn $20*x for his work on weekdays and $30*y for his work on weekends. The second sentence tells us that in this week, the total is $650. So, our first equation is:

20x + 30y = 650

The third sentence tells us that x is 5 times as many hours as y. In other words:

x = 5y

2) Solve for one of the variables. Now that you have 2 equations with 2 variables, you can manipulate the equations to cancel out one variable and solve for the other. Since the question asks for the number of weekend hours, let's solve for y.

Here, it's easier to just substitute x in the original equation. If you put 5y in place of x, the equation becomes:

(20*5y) + 30y = 650 
expand --> 
100y + 30y = 650
add --> 
130y = 650
divide both sides by 10 -->
13y = 65
divide both sides by 13 -->
y = 5

So, Ramiro worked 5 hours on the weekend (and therefore, 25 during the week). 

Wow. that is a really cool question.

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