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

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7 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:37) correct 33% (02:44) wrong based on 263 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

Originally posted by avohden on 22 Oct 2013, 20:00.
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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Joined: 02 Sep 2009
Posts: 58422
Re: Three years from now, Dathan will be three times as old as E  [#permalink]

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2
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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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.

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

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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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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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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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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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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

So whats given, x = Dathan, y = Ellen & z = Famke

x + 3 = 3y + 9

y + 3 = z - 3

x = 2z - 3

Now just manipulate above expressions to get

2z - 3y = 9 ----------(b)
z - y = 6------------(a)

Multiply (a) by 2 and then subtract from (b)
y = 3

z = 9

A
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: Three years from now, Dathan will be three times as old as E   [#permalink] 17 Feb 2019, 09:34
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