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# Three years from now, Dathan will be three times as old as E

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Director
Status: 1,750 Q's attempted and counting
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Three years from now, Dathan will be three times as old as E [#permalink]

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22 Oct 2013, 20:00
3
This post was
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Difficulty:

55% (hard)

Question Stats:

66% (03:28) correct 34% (02:47) wrong based on 184 sessions

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Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Oct 2013, 00:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Three years from now, Dathan will be three times as old as E [#permalink]

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23 Oct 2013, 00:57
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow

Three years from now, Dathan will be three times as old as Ellen: D + 3 = 3(E+3) --> D = 3E + 6.

Three years from now, Ellen will be six years younger than Famke: E +3 = (F + 3) - 6 --> E = F - 6.

Dathan's age (now) is three years less than twice Famke's age: D = 2F - 3.

From (I) and (III): 3E + 6 = 2F - 3 --> 3E = 2F - 9.
Since from (II) E = F - 6, then 3(F - 6) = 2F - 9 --> F = 9.

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Re: Three years from now, Dathan will be three times as old as E [#permalink]

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23 Oct 2013, 01:14
Bunuel wrote:
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow

Three years from now, Dathan will be three times as old as Ellen: D + 3 = 3(E+3) --> D = 3E + 6.

Three years from now, Ellen will be six years younger than Famke: E +3 = (F + 3) - 6 --> E = F - 6.

Dathan's age (now) is three years less than twice Famke's age: D = 2F - 3.

From (I) and (III): 3E + 6 = 2F - 3 --> 3E = 2F - 9.
Since from (II) E = F - 6, then 3(F - 6) = 2F - 9 --> F = 9.

Similar "age" problems to practice:
today-rose-is-twice-as-old-as-sam-and-sam-is-3-years-younger-131477.html
jack-is-now-14-years-older-than-bill-if-in-10-years-jack-144435.html
age-problem-m03q13-74810.html
if-father-s-age-is-1-less-than-twice-the-son-s-age-what-is-126832.html
john-is-20-years-older-than-brian-12-years-ago-john-was-132135.html
8-years-ago-george-was-half-as-old-as-sarah-sarah-is-now-132076.html
in-ten-years-david-will-be-four-times-as-old-as-aaron-twen-104243.html
roy-is-now-4-years-older-than-erik-and-half-of-that-amount-90386.html

Hope it helps.
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Re: Three years from now, Dathan will be three times... [#permalink]

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23 Oct 2013, 07:44
Official Explanation

Three years from now, Dathan's age will be d + 3, Ellen's will be e + 3, and Famke will be f + 3. Thus, three years from now, (d + 3) = 3(e + 3), and (e + 3) = (f + 3) - 6. We also know that d = 2f - 3 from the last sentence. Line up and simplify the equations:

d + 3 = 3e + 9, or d = 3e + 6 -----> e + 3 = f - 3 ------> d = 2f - 3

Since the first and third equations are set equal to d, combine them: 3e + 6 = 2f - 3

Now there are two equations, each of which has the same two variables, e and f: e + 3 = f - 3, or e = f - 6 ----> 3e + 6 = 2f - 3

Substitute the value of e from the first equation into the second:
3(f - 6) + 6 = 2f - 3 ----> 3f - 18 + 6 = 2f - 3 -----> 3f - 9 = 2f -----> f = 9, choice (A).

Hope it helps
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Re: Three years from now, Dathan will be three times as old as E [#permalink]

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25 Feb 2014, 03:18
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow

Let the present ages of Dathan, Ellen & Famke be d , e & f

So from the information given in the question, we get the following 3 equations:

d+3 = 3(e+3)
e = f-6
d = 2f - 3

Solving the above 3 equations, we get Famke = 9 yrs = Answer = A
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Re: Three years from now, Dathan will be three times as old as E [#permalink]

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28 Dec 2015, 16:35
D+3=3(E+3)
E+3=(F+3)-6
D=2F-3.

E+3=F-3 or E=F-6.
D+3=3(F-6+3)
D+3=3F-9
D=3F-12.
now, we have D=2F-3.

2F-3=3F-12
9=F.

F=9. A.
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Re: Three years from now, Dathan will be three times as old as E [#permalink]

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28 Dec 2015, 21:46
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow

We need to find Famke's age so say it is F.

Then Dathan's age = 2F - 3
Ellen's age = F - 6 (If in 3 yrs, Ellen will be 6 yrs younger than Famke, she must be 6 yrs younger today too)
Dathan + 3 = 3(F - 6 + 3)

So
2F - 3 = 3(F - 3) - 3
F = 9 yrs

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Re: Three years from now, Dathan will be three times as old as E [#permalink]

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10 Jan 2017, 11:07
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Re: Three years from now, Dathan will be three times as old as E   [#permalink] 10 Jan 2017, 11:07
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