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Manager  Joined: 22 Sep 2010
Posts: 71
Each week, Harry is paid x dollars per hour for the first 30 hours and  [#permalink]

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Difficulty:   15% (low)

Question Stats: 84% (02:16) correct 16% (02:55) wrong based on 396 sessions

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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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Joined: 02 Sep 2009
Posts: 58434
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.

Hope it's clear.
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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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Manager  Joined: 30 Aug 2010
Posts: 81
Location: Bangalore, India
Re: Each week, Harry is paid x dollars per hour for the first 30 hours and  [#permalink]

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42x=30x+1.5x(H-30)
==> 42=30+1.5(H-30)
==> H-30 = 24/3=8 ==> H = 38

Intern  Joined: 24 Jun 2010
Posts: 11
Re: Each week, Harry is paid x dollars per hour for the first 30 hours and  [#permalink]

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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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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

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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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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]

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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.

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: Each week, Harry is paid x dollars per hour for the first 30  [#permalink]

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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.

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]

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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]

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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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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

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Posts: 58434
Re: Each week, Harry is paid x dollars per hour for the first 30  [#permalink]

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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]

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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]

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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]

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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 Non-Human User Joined: 09 Sep 2013
Posts: 13241
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] 14 Apr 2019, 12:22
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