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# Last summer, Roger worked x days at 2 hours/day at a job, and he was

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Math Expert
Joined: 02 Sep 2009
Posts: 60480
Last summer, Roger worked x days at 2 hours/day at a job, and he was  [#permalink]

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28 May 2016, 06:10
00:00

Difficulty:

15% (low)

Question Stats:

93% (02:12) correct 7% (02:19) wrong based on 73 sessions

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Last summer, Roger worked x days at 2 hours/day at a job, and he was paid at a rate of r dollars per hour. For the whole summer, he earned $1000. This summer, he will work at another job that offers the same pay rate, r dollars per hour. This summer he will work H days at 5 hours/day, so that he will earn$4000 for the entire summer. In terms of x, which of the following equals H?

(A) x
(B) 2x/3
(C) 2x
(D) 4x/3
(E) 8x/5

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Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was  [#permalink]

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28 May 2016, 06:29
Bunuel wrote:
Last summer, Roger worked x days at 2 hours/day at a job, and he was paid at a rate of r dollars per hour. For the whole summer, he earned $1000. This summer, he will work at another job that offers the same pay rate, r dollars per hour. This summer he will work H days at 5 hours/day, so that he will earn$4000 for the entire summer. In terms of x, which of the following equals H?

(A) x
(B) 2x/3
(C) 2x
(D) 4x/3
(E) 8x/5

Last Summer story
Total hours: 2x
rate: $r per hour 2rx = 1000; rx = 500 This Summer story Total hours: 5H rate:$r per hour
Total payment = 5rH = 4000

5rH = 8 *500 = 8rx
5H=8x

H= $$\frac{8x}{5}$$

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Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was  [#permalink]

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28 May 2016, 06:35
Number of days Roger worked last summer = x
Hourly earning of Roger = r dollars
Number of hours worked in a day = 2
Total amount earned by Roger in last summer = 1000
(2r)* x = 1000
=> rx = 500 -- equation 1

This summer , number of hours worked in a day = 5
number of days = H
(5r)* H = 4000
=> rH = 800 -- equation 2
From equations 1 and 2 , we get
H/x = 8/5
=>H = (8/5)x
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Joined: 22 Mar 2014
Posts: 1
Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was  [#permalink]

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29 May 2016, 00:51
Rate (r) = Total Earning for the summer / Total number of hours Roger worked each summer

Since Rate (r) is equal for both summers -

Total Earning for the Summer1 / Total number of hours Roger worked each Summer1 = Total Earning for the Summer2 / Total number of hours Roger worked each Summer2

i.e. 1000/2x = 4000/5H

or , H = (4000 * 2X) / (1000 * 5)

or , H = (8/5)x

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Joined: 26 Mar 2013
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Concentration: Operations, Strategy
Schools: Erasmus '21 (M$) Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was [#permalink] ### Show Tags 29 May 2016, 13:40 Bunuel wrote: Last summer, Roger worked x days at 2 hours/day at a job, and he was paid at a rate of r dollars per hour. For the whole summer, he earned$1000. This summer, he will work at another job that offers the same pay rate, r dollars per hour. This summer he will work H days at 5 hours/day, so that he will earn $4000 for the entire summer. In terms of x, which of the following equals H? (A) x (B) 2x/3 (C) 2x (D) 4x/3 (E) 8x/5 Put r =10$/hr ...........then 1000= (2) (10) X......X=50 days

Use same value of r......then 4000=(5) (10) H.....H=80 days

H/X=8/5

Director
Joined: 20 Feb 2015
Posts: 734
Concentration: Strategy, General Management
Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was  [#permalink]

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30 May 2016, 03:56
x.2.r=1000 --1
h.5.r=4000 --2

or,

r=500/x=800/h

h=(8x/5)
Director
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Posts: 945
Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was  [#permalink]

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27 Aug 2018, 09:02
Bunuel wrote:
Last summer, Roger worked x days at 2 hours/day at a job, and he was paid at a rate of r dollars per hour. For the whole summer, he earned $1000. This summer, he will work at another job that offers the same pay rate, r dollars per hour. This summer he will work H days at 5 hours/day, so that he will earn$4000 for the entire summer. In terms of x, which of the following equals H?

(A) x
(B) 2x/3
(C) 2x
(D) 4x/3
(E) 8x/5

Dear Moderator,

Came across this question while going through Algebra, please can you confirm the OA for this one?Thank you.
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Re: Last summer, Roger worked x days at 2 hours/day at a job, and he was   [#permalink] 27 Aug 2018, 09:02
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