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Each week, Harry is paid x dollars per hour for the first 30

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pzazz12
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Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink] New post   01 Oct 2010, 04:36
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Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

A. 35
B. 36
C. 37
D. 38
E. 39
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D
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Bunuel
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   28 Apr 2012, 16:15
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enigma123 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, ho wmany hours did Harry work last week?

A. 35
B. 36
C. 37
D. 38
E. 39


James worked for 41 hours hence he earned 40*x+1*2x=42x dollars;

We know that Harry also earned the same 42x dollars, out of which he earned 30x dollars for the first 30 hours plus 12x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 12x/1.5x=8 additional hours, so Harry worked for total of 30+8=38 hours.

Answer: D.

Hope it's clear.
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Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   28 Apr 2012, 14:07
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Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, ho wmany hours did Harry work last week?

A. 35
B. 36
C. 37
D. 38
E. 39
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muralimba
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Re: Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink] New post   01 Oct 2010, 04:44
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42x=30x+1.5x(H-30)
==> 42=30+1.5(H-30)
==> H-30 = 24/3=8 ==> H = 38

Answer id "D"
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Re: Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink] New post   04 Jan 2011, 23:52
30x+1.5x(T-30)=40X+2x

Total hrs(T)=38
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Re: Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink] New post   05 Jan 2011, 00:16
ChenggongMAS wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?

A. 35
B. 36
C. 37
D. 38
E. 39

I almost understand the OG's explanation; however, there is one number that I do not understand in the equation. I will elaborate after a few responses are posted. I do not want to ruin the question for someone with a "hint".

~Chenggong


James worked 41 hours, so he was paid 40x+1(2x)
Lets say Harry worked h hours. Since he was paid the same as Harry, which is more than 30x (42x), he mus have worked more than 30 hours, hence h>30
Harry got paid : 30x+(h-30)1.5x

We know : 30x + (h-30)1.5x=42x
1.5hx -15x = 42x
1.5hx -57x = 0
(1.5h - 57)x=0
h = 57/1.5 = 38

Answer is (d)
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Re: Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink] New post   05 Jan 2011, 00:42
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Is the following approach ok?

James got paid : 40x+2x = 42x

harry : 30x+ (1.5x)Y ... Y are the additional hours that harry put in after 30 hrs of work.

42x = 30x + (1.5x)Y

12x = (1.5x)Y

Y = 12/1.5 = 8

Total hours = 30+8 = 38.
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   07 May 2012, 17:30
Bunuel wrote:
enigma123 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, ho wmany hours did Harry work last week?

A. 35
B. 36
C. 37
D. 38
E. 39


James worked for 41 hours hence he earned 40*x+1*2x=42x dollars;

We know that Harry also earned the same 42x dollars, out of which he earned 30x dollars for the first 30 hours plus 12x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 12x/1.5x=8 additional hours, so Harry worked for total of 30+8=38 hours.

Answer: D.

Hope it's clear.


Hi Bunuel,
could you please tell me why my approach is incorrect.
Total hours worked by Harry is H
Number of additional hours = H-30
Total earned by James is 42 as you calculated

30x+(H-30)1.5x = 42x
(H-30)1.5x=12x= 1.5x -45=12= x=67/1.5==44 hours
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   08 May 2012, 01:15
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jayaddula wrote:
Bunuel wrote:
enigma123 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, ho wmany hours did Harry work last week?

A. 35
B. 36
C. 37
D. 38
E. 39


James worked for 41 hours hence he earned 40*x+1*2x=42x dollars;

We know that Harry also earned the same 42x dollars, out of which he earned 30x dollars for the first 30 hours plus 12x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 12x/1.5x=8 additional hours, so Harry worked for total of 30+8=38 hours.

Answer: D.

Hope it's clear.


Hi Bunuel,
could you please tell me why my approach is incorrect.
Total hours worked by Harry is H
Number of additional hours = H-30
Total earned by James is 42 as you calculated

30x+(H-30)1.5x = 42x
(H-30)1.5x=12x= 1.5x -45=12= x=67/1.5==44 hours


Equation is correct, math is not: 30x+(H-30)1.5x=42x--> (H-30)1.5=12 --> H-30=8 --> H=38.

Hope it's clear.
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   31 May 2013, 06:22
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   02 Jun 2013, 12:56
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James worked a total of 41 hours, hence James earned amount = 40x + 2x = 42x

Harry and James were paid the same amount last week.Let y be the number of additional hours that Harry has worked over and above the 30 hrs

therefore 42x = 30x (amount Harry earned for the first 30 hours) + 1.5xy

12x = 1.5xy

Hence, y = 8

Since y is the incremental number of hours that Harry has worked,

Harry has worked a total of 30 + 8 = 38 hours last week
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   03 Jun 2013, 02:24
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I used simple substitution.
Let's assume both of them are paid 10 $ per hour.
Since Harry and James are paid the same amount then :
10*30+1.5*10*t (time)= 10*40+20 (we know that James worked for total 41 hours)
300+15t=420
t=8 hours ==> Harry worked for 30+8 = 38 hours

Answer: D
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   28 Dec 2017, 04:52
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Thereces wrote:
Hi there! I agree with those who write that the right answer is D. But which one really is, dear author? :)


You can check the Official Answer (OA) under the spoiler in the original post.
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Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   Updated on: 23 Feb 2018, 13:13
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pzazz12 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

A. 35
B. 36
C. 37
D. 38
E. 39


Yay ! i have the most fantastic solution :)

let x = dollars
y = hours

Hary 30x+1.5x
James 40x + 2x

so say 1 dollar is hourly wage ---> If James earned $ 42 then Harry 30 +(1.5*8) = 38 hours :)

Originally posted by dave13 on 23 Feb 2018, 12:00.
Last edited by dave13 on 23 Feb 2018, 13:13, edited 1 time in total.
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Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   23 Feb 2018, 12:58
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dave13 wrote:
pzazz12 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

A. 35
B. 36
C. 37
D. 38
E. 39

Yay ! i have the most fantastic solution :)

let x = dollars
y = hours

Hary 30x+1.5x
James 40x-2x

so say 1 dollar is hourly wage ---> If James earned $ 42 then Harry 30 +(1.5*8) = 38 hours :)

Nice work. Just one typo that might confuse someone. :-)
James is 40x + 2x.
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   23 Feb 2018, 13:12
generis wrote:
dave13 wrote:
pzazz12 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

A. 35
B. 36
C. 37
D. 38
E. 39

Yay ! i have the most fantastic solution :)

let x = dollars
y = hours

Hary 30x+1.5x
James 40x-2x

so say 1 dollar is hourly wage ---> If James earned $ 42 then Harry 30 +(1.5*8) = 38 hours :)

Nice work. Just one typo that might confuse someone. :-)
James is 40x + 2x.


Hello generis, :) thanks ! i will edit it. you know what i like about you ? :) your sharp eye :)
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   27 Mar 2020, 05:12
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pzazz12 wrote:
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

A. 35
B. 36
C. 37
D. 38
E. 39


Last week, James worked a total of 41 hours, and thus he earned 40x + 2x = 42x dollars. We can let h = the total number of hours Harry worked last week and create the equation:

30x + 1.5x(h - 30) = 42x

30x + 1.5xh - 45x = 42x

1.5xh - 15x = 42x

1.5xh = 57x

1.5h = 57

h = 57/1.5 = 38

Answer: D
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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink] New post   18 Dec 2023, 09:31
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