Question

Vivienne someone earned 513.60 in a week. For her job, she is paid $19.75 for the first 20 hours of work, and then time and a half for every hour after that. How many hours did Vivienne work in the week?

Answer 1

Vivienne worked 24 hours in the week.

Explanation:

To find out how many hours Vivienne worked in the week, we can first calculate her earnings for the first 20 hours of work. She is paid $19.75 per hour for the first 20 hours, so her earnings for the first 20 hours are:

• 
  `\tt{20 * 19.75 = 395}`

Now, we need to find out how much she earned for the hours she worked after the first 20 hours. Since she earned $513.60 in total for the week, her earnings for the hours after the first 20 hours are:

• 
  `\tt{513.60 - 395 = 118.60}`

For the hours after the first 20 hours, she is paid time and a half, which means her hourly rate for these hours is:

• 
  `\tt{19.75 * 1.5 = 29.625}`

Now, we can calculate the number of hours she worked after the first 20 hours by dividing her earnings for these hours by her hourly rate for these hours:

• 
  `\tt{(118.60)/(29.625) = 4}`

So, Vivienne worked 4 hours after the first 20 hours. In total, she worked:

• 
  `\tt{20 + 4 = 24}`

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