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

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Carcass
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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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E

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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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E
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vidhikakani
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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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msh104
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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.
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Re: Employee X is paid $ 19.50 an hour no matter how many hours [#permalink] New post   17 Feb 2021, 09:21
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As they worked the same number of hours, there is no way they will be paid the same amount of money for working less than 40 hours (because Y is being paid less per hour working up to 40 hours). So, eliminate answer choices A, B, and C.

Now, you have a 50/50 shot. The best approach here is to back solve using the answer choices, testing out one option will lead you to the right answer eventually. Okay, Let's start with D, that means they worked for 42 hours.

So, A will be paid the amount of 42 * 19.5 = 819 $
and, B will be paid the amount of 40 * 18 + 2 * 18 * 1.5 = 774 $
That means they are not getting paid the same amount for working 42 hours.

Now, you can safely choose answer choice E.
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Employee X is paid $ 19.50 an hour no matter how many hours [#permalink] New post   17 Feb 2021, 10:43
Carcass wrote:
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

Kudos for the right answer and explanation


Let the number of additional hours be x
so,
19.5(40+x)=(18)(40)+(1.5)(18)x
780+19.5x=720+27x
60=7.5x
x=8

So, a total of (40 + x) = 48 hours

Hence, option E
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Employee X is paid $ 19.50 an hour no matter how many hours [#permalink]
17 Feb 2021, 10:43
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