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Every week, Renee is paid $40 per hour for the first 40 hours she work

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Every week, Renee is paid $40 per hour for the first 40 hours she work  [#permalink]

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New post 26 Aug 2018, 21:24
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Every week, Renee is paid $40 per hour for the first 40 hours she works, and $80 per hour for each hour she works after the first 40 hours. How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week?

(A) 60
(B) 65
(C) 70
(D) 75
(E) 80

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Re: Every week, Renee is paid $40 per hour for the first 40 hours she work  [#permalink]

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New post 26 Aug 2018, 21:39
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Bunuel wrote:
Every week, Renee is paid $40 per hour for the first 40 hours she works, and $80 per hour for each hour she works after the first 40 hours. How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week?

(A) 60
(B) 65
(C) 70
(D) 75
(E) 80


Renee makes $40*40 hours=$1600 in first 40 hours
Let 't' be the no of hours Renee would work.
Given, Renee makes $80 per hour for each hour she works after the first 40 hours. So, she makes an additional pay $80*(t-40)hours for every hour after 40 hours.

So, \(\frac{1600+80(t-40)}{t}=60\)
Or, 1600+80t-3200=60t
Or, 20t=1600
or, t=80 hours

Ans. (E)
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Re: Every week, Renee is paid $40 per hour for the first 40 hours she work  [#permalink]

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New post 26 Aug 2018, 22:22
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PKN wrote:
Bunuel wrote:
Every week, Renee is paid $40 per hour for the first 40 hours she works, and $80 per hour for each hour she works after the first 40 hours. How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week?

(A) 60
(B) 65
(C) 70
(D) 75
(E) 80


Renee makes $40*40 hours=$1600 in first 40 hours
Let 't' be the no of hours Renee would work.
Given, Renee makes $80 per hour for each hour she works after the first 40 hours. So, she makes an additional pay $80*(t-40)hours for every hour after 40 hours.

So, \(\frac{1600+80(t-40)}{t}=60\)
Or, 1600+80t-3200=60t
Or, 20t=1600
or, t=80 hours

Ans. (E)

PKN
Hi, Could you explain this part " So, she makes an additional pay $80*(t-40)hours for every hour after 40 hours.".
The way I was looking at it was:
Let x be the extra hours worked,
so to make the average equal to 60,
In the first 40 hours, amount earned = 1600.
Next x hours, amount earned = 80x (Since per hour = $80 after first 40 hrs)

(1600 +80x) / (40 + x) = 60
But on solving this I get 20x = 800 and x = 40 which is not in the options.
Could you please explain where am I going wrong?
Thanks a lot.
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Re: Every week, Renee is paid $40 per hour for the first 40 hours she work  [#permalink]

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New post 26 Aug 2018, 22:29
1
Sreyoshi007 wrote:
PKN wrote:
Bunuel wrote:
Every week, Renee is paid $40 per hour for the first 40 hours she works, and $80 per hour for each hour she works after the first 40 hours. How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week?

(A) 60
(B) 65
(C) 70
(D) 75
(E) 80


Renee makes $40*40 hours=$1600 in first 40 hours
Let 't' be the no of hours Renee would work.
Given, Renee makes $80 per hour for each hour she works after the first 40 hours. So, she makes an additional pay $80*(t-40)hours for every hour after 40 hours.

So, \(\frac{1600+80(t-40)}{t}=60\)
Or, 1600+80t-3200=60t
Or, 20t=1600
or, t=80 hours

Ans. (E)

PKN
Hi, Could you explain this part " So, she makes an additional pay $80*(t-40)hours for every hour after 40 hours.".
The way I was looking at it was:
Let x be the extra hours worked,
so to make the average equal to 60,
In the first 40 hours, amount earned = 1600.
Next x hours, amount earned = 80x (Since per hour = $80 after first 40 hrs)

(1600 +80x) / (40 + x) = 60
But on solving this I get 20x = 800 and x = 40 which is not in the options.
Could you please explain where am I going wrong?
Thanks a lot.


Hi Sreyoshi007,
You are absolutely correct.

Your x=No of additional hours=40.

Question stem:-How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week. ALREADY SHE HAS WORKED FOR 40 HOURS.

So, total no of hours she would work in a week=first 40 hours+additional hours=40+x=40+40=80

Hope it helps.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
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Joined: 01 Feb 2018
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Re: Every week, Renee is paid $40 per hour for the first 40 hours she work  [#permalink]

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New post 26 Aug 2018, 22:35
Quote:
Hi Sreyoshi007,
You are absolutely correct.

Your x=No of additional hours=40.

Question stem:-How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week. ALREADY SHE HAS WORKED FOR 40 HOURS.

So, total no of hours she would work in a week=first 40 hours+additional hours=40+x=40+40=80

Hope it helps.


PKN Thanks a lot, I got it now. I should have re-read the question stem more carefully.
_________________
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Re: Every week, Renee is paid $40 per hour for the first 40 hours she work  [#permalink]

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New post 26 Aug 2018, 23:29
1
Sreyoshi007 wrote:
Quote:
Hi Sreyoshi007,
You are absolutely correct.

Your x=No of additional hours=40.

Question stem:-How many hours would Renee have to work in one week to earn an average (arithmetic mean) of $60 per hour that week. ALREADY SHE HAS WORKED FOR 40 HOURS.

So, total no of hours she would work in a week=first 40 hours+additional hours=40+x=40+40=80

Hope it helps.


PKN Thanks a lot, I got it now. I should have re-read the question stem more carefully.


You are welcome Sreyoshi007,

I would suggest, there are two ways you can avoid these kind of situations.
1) Write down the question stem at first glance. (WHAT IS ASKED or WHAT IS OUR REQUIREMENT)
2) Always try to assign the variable to your requirement. (For example, here our requirement was "total no of hours". So, assign x or t =Total no of hours)
Merit:- After solving, the value of the variable would direct you to the correct answer option.
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Re: Every week, Renee is paid $40 per hour for the first 40 hours she work   [#permalink] 26 Aug 2018, 23:29
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