Alice earns 2 times her normal hourly rate for each hour she works after 40 hours in a week. She worked 50 hours this week and earned $660.
What is her normal hourly rate?
x = Her normal hourly rate
She worked 50 - 40 = 10 hours more of her normal hourly rate.
She earned 40 x for her normal hourly rate + 10 ∙ 2 her normal hourly rate
40 x + 10 ∙ 2 x = 660
40 x + 20 x = 660
60 x = 660
x = 660 / 60
x = $11
Let's denote Alice's normal hourly rate as x dollars per hour.
From the given information, we know that Alice worked 50 hours this week.
For the first 40 hours, Alice earned x dollars per hour. So, the total amount Alice earned for the first 40 hours is 40 * x = 40x dollars.
For the remaining 10 hours (50 total hours - 40 hours), Alice earned 2 times her normal hourly rate. So, the total amount Alice earned for the remaining 10 hours is 2x * 10 = 20x dollars.
Adding these two amounts together, we get the total amount Alice earned: 40x + 20x = 60x dollars.
We are also given that Alice earned $660 in total.
Therefore, we can set up an equation:
60x = 660.
To find x, we divide both sides of the equation by 60:
60x/60 = 660/60,
x = 11.
Therefore, Alice's normal hourly rate is $11 per hour.
To find Alice's normal hourly rate, we need to first determine the number of hours she worked that are eligible for the increased rate, which is any hour worked after 40 hours in a week.
Given that Alice worked a total of 50 hours, the number of hours that exceed 40 is 50 - 40 = 10 hours.
Now, we know that Alice earns 2 times her normal hourly rate for each hour she works after 40 hours in a week. Therefore, for each of the 10 extra hours worked, she earned her normal hourly rate multiplied by 2.
Let's denote Alice's normal hourly rate as x. So for the extra 10 hours, she earned 10 * 2x = 20x.
We also know that Alice earned a total of $660 for the week. This amount includes both her normal hourly rate for the first 40 hours and the increased rate for the extra 10 hours.
Since Alice's normal hourly rate is x, her earnings for the first 40 hours would be 40x.
Thus, the total earnings can be expressed as the sum of her earnings for the first 40 hours and the extra 10 hours, which is 40x + 20x = 60x.
We can set up an equation based on this information:
40x + 20x = 660
Combining like terms, we get:
60x = 660
To solve for x, we divide both sides of the equation by 60:
x = 660 / 60
Calculating the result, we find:
x = $11
Therefore, Alice's normal hourly rate is $11.