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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

2

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A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

69% (03:25) correct
31% (02:45) wrong based on 137 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?

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

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23 Oct 2013, 00:57

Expert's post

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.

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

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23 Oct 2013, 01:14

Expert's post

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.

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

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23 Oct 2013, 07:44

Official Explanation

Answer: A 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).

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 _________________

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

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28 Dec 2015, 21:46

Expert's post

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)

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