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Anthony and Cindy were each given x dollars in advance to pe

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Anthony and Cindy were each given x dollars in advance to pe [#permalink]

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Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?

A. 2y
B. 4y
C. 5y
D. 6y
E. 10y
[Reveal] Spoiler: OA

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Re: ratios [#permalink]

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New post 19 Sep 2010, 16:14
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We know that

(X+y)/14 = (x-y)/10 (equating the money per day)
So 4x = 24y OR x=6y
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Re: ratios [#permalink]

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New post 19 Sep 2010, 16:47
Nice one. I missed (X+y)/14 when making equation
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mrinal2100 wrote:
Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance,in terms of y?
a)2y
B)4y
C)5y
D)6y
E)10y


Anthony performed for 14 days meansw Cindy performed for(14-4)=10 days.

If Cindy gives y dollars to Anthony their Daily rate will be equal.It means

(x+y)/14=(x-y)/10
Solving we get, x=6y

Now Anthony's Advance is x=6y .So answer should be D.

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Re: word problem [#permalink]

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mrinal2100 wrote:
Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance,in terms of y?
a)2y
B)4y
C)5y
D)6y
E)10y


Anthony performed for 14 days, and Cindy for 10 days. Cindy gives Anthony y dollars to make the daily rate equal.
Anthony's rate = Cindy's rate
(x+y)/14=(x-y)/10
10x+10y=14x-14y
4x=24y
x=4y

Answer is (d)
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Re: Anthony and Cindy were each given x dollars in advance to pe [#permalink]

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New post 17 Dec 2013, 03:42
zisis wrote:
Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?

A. 2y
B. 4y
C. 5y
D. 6y
E. 10y


This is a "stolen" question from OG:
Quote:
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

(A) 4y
(B) 5y
(C) 6y
(D) 8y
(E) 9y


Discussed here: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html

All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html
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Re: Anthony and Cindy were each given x dollars in advance to pe [#permalink]

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New post 17 Dec 2013, 07:47
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zisis wrote:
Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?

A. 2y
B. 4y
C. 5y
D. 6y
E. 10y


The amount Cindy has in the end is x-y dollars and she worked for 10 days;
The amount Anthony has in the end is x+y dollars and he worked for 14 days;

We are told that in this case their daily rate was the same: \(daily \ rate=\frac{payment}{# \ of \ days \ worked}=\frac{x-y}{10}=\frac{x+y}{14}\), from \(\frac{x-y}{10}=\frac{x+y}{14}\) we get that \(x=6y\).

Answer: D.
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Re: Anthony and Cindy were each given x dollars in advance to pe [#permalink]

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New post 17 Dec 2013, 23:48
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zisis wrote:
Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?

A. 2y
B. 4y
C. 5y
D. 6y
E. 10y


You can also solve it by using easy numbers.

Anthony works for 14 days. Cindy works for 10 days. Say, the daily rate is $1/day which would mean that finally Anthony has $14 and finally Cindy has $10. Now it's obvious that they both would have received $12 and Cindy would have given Anthony $2 so that she would have $10 while Anthony would have $14.
So y = $2 (Amount given by Cindy to Anthony)
Advance paid to Anthony = $12 = 6*2 = 6y
Answer (D)
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Re: Anthony and Cindy were each given x dollars in advance to pe [#permalink]

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New post 06 May 2015, 18:00
(x+y) / 14 = (x-y) / 10, solve and you get x =6y answer is D

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