How do I solve this question?
"Rory Gilmore earns $20 per hour during the week and $30 per hour for overtime on the weekends. One week Rory earned a total of $650. She worked 5 times as many hours during the week as she did on the weekend. Write and solve an equation or system of equations to determine how many hours of overtime Rory worked on the weekend."
So far I got 20X+30Y=650. I know that X=25 and Y=5 but I cant show my work to show how I got that answer. Anyone know how I can solve this algebraically to get my answer?
x = Overtime hrs
30x = Overtime wages
5x = Regular hrs
20(5x) = Regular wages
30x + 20(5x) = 650
30x + 100x = 650
130x = 650
x = 5 overtime hours
30 * 5 = $150 OT pay
20 * 25 = $500 Reg pay
Total 30 hrs = $650
To solve this problem algebraically, we can set up a system of equations based on the given information.
Let's define:
X = the number of hours Rory worked during the week
Y = the number of hours Rory worked on the weekend
From the problem statement, we know:
1) Rory earns $20 per hour during the week, so the amount earned during the week is 20X.
2) Rory earns $30 per hour for overtime on the weekends, so the amount earned for overtime on the weekend is 30Y.
3) The total amount Rory earned is $650, so we have the equation: 20X + 30Y = 650.
Additionally, we are given the ratio between the hours worked during the week and on the weekend:
4) Rory worked 5 times as many hours during the week as on the weekend, so we have the equation: X = 5Y.
Now, we have a system of two equations with two variables:
Equation 1: 20X + 30Y = 650
Equation 2: X = 5Y
To solve this system algebraically, we can substitute X from Equation 2 into Equation 1:
20(5Y) + 30Y = 650
100Y + 30Y = 650
130Y = 650
Y = 5
Now, substituting the value of Y back into Equation 2, we can solve for X:
X = 5Y
X = 5(5)
X = 25
Therefore, the solution to the system of equations is X = 25 and Y = 5. It means that Rory worked 25 hours during the week and 5 hours on the weekend.