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

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Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink]

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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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Re: Each week, Harry is paid x dollars per hour for the first 30 hours and [#permalink]

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New post 01 Oct 2010, 04:44
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]

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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]

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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]

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New post 05 Jan 2011, 00:42
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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Each week, Harry is paid x dollars per hour for the first 30 [#permalink]

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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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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink]

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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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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink]

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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]

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New post 08 May 2012, 01:15
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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink]

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Re: Each week, Harry is paid x dollars per hour for the first 30 [#permalink]

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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]

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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 hours and   [#permalink] 23 Aug 2016, 04:45
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