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Employee X is paid $ 19.50 an hour no matter how many hours

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Employee X is paid $ 19.50 an hour no matter how many hours [#permalink] New post 08 Sep 2019, 08:34
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Employee X is paid $ 19.50 an hour no matter how many hours he works per week. Employee Y is paid $ 18 an hour for the first 40 hours she works in a week and is paid 1.5 times the hourly rate for every additional hour she works. On a certain week, both employees worked the same number of hours and were paid the same amount. How many hours did each employee work that week?

A. 32

B. 36

C. 40

D. 42

E. 48

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[Reveal] Spoiler: OA

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Re: Employee X is paid $ 19.50 an hour no matter how many hours [#permalink] New post 28 Sep 2019, 02:40
How?? can u please explain??
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Re: Employee X is paid $ 19.50 an hour no matter how many hours [#permalink] New post 29 Sep 2019, 23:18
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Let x be the number of hours Employee X worked, and y be the number of hours Employee Y worked in that week.

With two unknown variables, we need two equations.

Equation 1: x = y, since the question states they worked the same number of hours.

Equation 2: $19.5x = $18(40 hours) + $27 (y -40 hours). This is the mathematical statement of the second sentence and the third sentence part that states Employee X and Employee Y were paid the same amount. $18(40 hours) is the amount Employee Y was paid in the first 40 hours, and $27 (y - 40 hours) is the amount Y was paid after the first 40 hours; $27 comes about from 1.5 times $18 (or in other words, $18 + 9 = $27).

Put Equation 1, x = y, into Equation 2 and it becomes $19.5x =$18 (40 hours) + $27(x - 40 hours). Now, solve for x.

$19.5x =$18 (40 hours) + $27(x - 40 hours)
$19.5x = 720 ($·hours) + $27x - 1080 ($·hours)
-$7.5x = -360 ($·hours)
x = 48 hours

This means the total number of hours Employee X worked is x, and x = 48 hours. Since per the question, both employees' worked the same number of hours, Employee Y also worked 48 hours.

48 hours is Choice E.
Re: Employee X is paid $ 19.50 an hour no matter how many hours   [#permalink] 29 Sep 2019, 23:18
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Employee X is paid $ 19.50 an hour no matter how many hours

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