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# The sum of the ages of Doris and Fred is y years. If Doris

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The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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24 Feb 2014, 23:07
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred , how many years old will Fred be y years from now, in terms of y ?

(A) y - 6
(B) 2y - 6
(C) y/2 - 6
(D) 3y/2 - 6
(E) 5y/2 - 6

Problem Solving
Question: 115
Category: Algebra Applied problems; Simultaneous equations
Page: 76
Difficulty: 600

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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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24 Feb 2014, 23:07
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SOLUTION

The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred , how many years old will Fred be y years from now, in terms of y ?

(A) y - 6
(B) 2y - 6
(C) y/2 - 6
(D) 3y/2 - 6
(E) 5y/2 - 6

The sum of the ages of Doris and Fred is y years: d + f = y;
Doris is 12 years older than Fred: d = f + 12.

Subtract one from another: f = y - f - 12 --> f = y/2 - 6.

y years from now, Fred will be f + y = y/2 - 6 + y = 3y/2 - 6 years old.

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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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25 Feb 2014, 01:12
2
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Let the ages of Fred and Doris be 'F' and 'D' respectively.

Sum of their ages = F+D = y
Now since Doris is 12 years older than Fred , D=F+12
Therefore 2F+12=y
thus F=y/2 - 6

'y' years from now Fred will be F=y/2-6+ y = 3y/2 -6

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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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25 Feb 2014, 21:15
2
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Let the ages of Doris and Fred be D and F respectively.

Given that, D + F = y & D = F + 12;
F + 12 + F = y;
2F + 12 = y;
2F = y - 12;
F = y/2 - 6;

Now, since we are asked for Fred's age "y" years from now, we can add y to F:
F + y = y + y/2 - 6;
F + y = 3y/2 - 6;

Ans is (D).
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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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26 Feb 2014, 01:06
1
KUDOS
Option D.
D+F=y
And D=F+12
Therefore,2F+12=y
Or F=(y-12)/2
After y years,F=y+(y-12)/2
F=3y/2-6
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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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01 Mar 2014, 03:39
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SOLUTION

The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred , how many years old will Fred be y years from now, in terms of y ?

(A) y - 6
(B) 2y - 6
(C) y/2 - 6
(D) 3y/2 - 6
(E) 5y/2 - 6

The sum of the ages of Doris and Fred is y years: d + f = y;
Doris is 12 years older than Fred: d = f + 12.

Subtract one from another: f = y - f - 12 --> f = y/2 - 6.

y years from now, Fred will be f + y = y/2 - 6 + y = 3y/2 - 6 years old.

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
three-years-from-now-dathan-will-be-three-times-as-old-as-e-162041.html
if-mario-was-32-years-old-8-years-ago-how-old-was-he-x-year-164898.html
what-is-ricky-s-age-now-165766.html
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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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13 Apr 2014, 06:10
D+F = Y ---------------------- First Equation.

D=F+12 ---------------------- Second Equation

how many years old will Fred be y years from now

can be represented as (F+Y).

As we need the answer in terms of Y , substitute Second Equation in First.

F+12+F= Y;
2F+12=Y.
2F=Y-12
F=Y-12/2;

Now F+Y in terms of Y is Y-12/2 + Y = 3Y/2 -6 ;
Hence D
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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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13 Apr 2014, 19:34
Let age of Doris = d, then
Age of Fred = y-d .......... (1)

Doris is 12 yrs older than Fred

y-d+12 = d

2d = y+12

$$d = \frac{y}{2} + 6$$ ......... (2)

Substituting value of d from (2) in (1)

$$Age of Fred = y - (\frac{y}{2} + 6)$$

$$= \frac{y}{2} - 6$$

Age of Fred after y yrs

$$=\frac{y}{2} - 6 + y$$

$$= \frac{3y}{2} - 6$$

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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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11 Jun 2014, 13:41
It can be easily solved using smart numbers
Doris = D, Fred = F
Let's say D = 24 than F is 12 less = 12 --> 24 + 12 = Y = 36; So in Y or 36 Years Fred will be 12 + 36 = 48
Plugin 36 for Y, in a right answer you schould get 48 --> D (3*36)/2-6 = 48
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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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28 Jun 2015, 15:23
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Re: The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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05 Jul 2016, 23:57
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The sum of the ages of Doris and Fred is y years. If Doris [#permalink]

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09 Dec 2016, 02:46
BrainLab wrote:
It can be easily solved using smart numbers
Doris = D, Fred = F
Let's say D = 24 than F is 12 less = 12 --> 24 + 12 = Y = 36; So in Y or 36 Years Fred will be 12 + 36 = 48
Plugin 36 for Y, in a right answer you schould get 48 --> D (3*36)/2-6 = 48

I tried this method and I am completely stumped.

3*36=108
2-6=-4

108/4=27 not 48.

Can somebody please explain what I am doing wrong?
The sum of the ages of Doris and Fred is y years. If Doris   [#permalink] 09 Dec 2016, 02:46
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