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 determine how many hours of overtime Ramiro worked on the weekend.

20(5x) + 30x = 650

To solve this problem, let's use a system of equations. Let's represent the number of hours Ramiro worked during the week as "w" and the number of hours he worked on the weekend as "e".

From the given information, we know that Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekend. We also know that he earned a total of $650 in one week.

Equation 1: $20w + $30e = $650

Additionally, we are given that Ramiro worked 5 times as many hours during the week as he did on the weekend. That means we can write the following equation:

Equation 2: w = 5e

Now we have a system of equations:

Equation 1: $20w + $30e = $650
Equation 2: w = 5e

To solve this system, we can substitute the value of w from Equation 2 into Equation 1:

$20(5e) + $30e = $650

Simplifying this equation, we have:

$100e + $30e = $650
$130e = $650
e = $650 / $130
e = 5

So Ramiro worked 5 hours of overtime on the weekend.

Let's say Ramiro worked x hours on the weekend, so he worked 5x hours during the week.

His earnings from working during the week would be 20 * (5x) = 100x dollars.
His earnings from working on the weekend would be 30 * x = 30x dollars.
According to the problem, his total earnings for the week were $650.
So we can write the equation: 100x + 30x = 650
Combining like terms, we get: 130x = 650
Dividing both sides by 130, we find: x = 5
Therefore, Ramiro worked 5 hours of overtime on the weekend.