Systems of Equations : GMAT Problem Solving (PS)
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# Systems of Equations

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Systems of Equations [#permalink]

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04 Jan 2011, 21:07
00:00

Difficulty:

35% (medium)

Question Stats:

80% (02:03) correct 20% (01:16) wrong based on 10 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 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
[Reveal] Spoiler: OA
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Re: Systems of Equations [#permalink]

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04 Jan 2011, 22:52
30x+1.5x(T-30)=40X+2x

Total hrs(T)=38
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Re: Systems of Equations [#permalink]

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04 Jan 2011, 23:16
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

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Re: Systems of Equations [#permalink]

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04 Jan 2011, 23:42
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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Re: Systems of Equations [#permalink]

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05 Jan 2011, 06:08
Thank you kanhaiya, shrouded1, and swaraj! I was getting stuck on the 42x. I know understand it which makes this problem very simple.

~Chenggong
Re: Systems of Equations   [#permalink] 05 Jan 2011, 06:08
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# Systems of Equations

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