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# Two years ago, Cecilia's mother was three times as old as Cecilia. In

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Joined: 02 Sep 2009
Posts: 58320
Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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17 Jan 2018, 00:11
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:52) correct 30% (01:53) wrong based on 70 sessions

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Two years ago, Cecilia's mother was three times as old as Cecilia. In 12 years, Cecilia's mother will be twice as old as Cecilia. How old is Cecilia currently?

A. 10
B. 12
C. 14
D. 16
E. 18

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Re: Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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17 Jan 2018, 01:00
1
Two years ago
Mother = 3x
Cecilia = x

Now
Mother = 3x+2
Cecilia = x+2

12 years from now
Mother = 3x+14
Cecilia = x+14

3x+14 =2(x+14)
3x+14=2x+28
x=14

Cecilia today’s age is x+2=14+2=16
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Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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19 Jan 2018, 08:48
2
Bunuel wrote:
Two years ago, Cecilia's mother was three times as old as Cecilia. In 12 years, Cecilia's mother will be twice as old as Cecilia. How old is Cecilia currently?

A. 10
B. 12
C. 14
D. 16
E. 18

C = Cecilia
M = Mother

Two years ago:
C's mother was three times as old as C
M - 2 = 3(C - 2)
M - 2 = 3C - 6
M = 3C - 4 ---> Use this for next equation

In 12 years:
C's mother will be twice as old as C
M + 12 = 2(C + 12) - substitute
(3C - 4) + 12 = 2C + 24
C = 16

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Re: Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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19 Jan 2018, 10:38
generis wrote:
Bunuel wrote:
Two years ago, Cecilia's mother was three times as old as Cecilia. In 12 years, Cecilia's mother will be twice as old as Cecilia. How old is Cecilia currently?

A. 10
B. 12
C. 14
D. 16
E. 18

C = Cecilia
M = Mother

Two years ago:
C's mother was three times as old as C
M - 2 = 3(C - 2)
M - 2 = 3C - 6
M = 3C - 4 ---> Use this for next equation

In 12 years:
C's mother will be twice as old as C
M + 12 = 2(C + 12) - substitute
(3C - 4) + 12 = 2C + 24
C = 16

Hello generis, can you advice if my approach is correct

C = Cecilia
M = Mother

m=3c-2 <---- Two years ago, Cecilia's mother was three times as old as Cecilia
m=12+2c < ---- In 12 years, Cecilia's mother will be twice as old as Cecilia

How old is Cecilia currently? <--- C ?

3c-2 = 12+2c
3c-2c = 12+2
c= 14

Since two years ago, Cecilia's mother was three times as old as Cecilia - 2, so we add those two years to 14 and get 16 no ? I think I missed something though I answered correctly
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Posts: 3536
Re: Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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19 Jan 2018, 15:34
1
dave13 wrote:
Bunuel wrote:
Two years ago, Cecilia's mother was three times as old as Cecilia. In 12 years, Cecilia's mother will be twice as old as Cecilia. How old is Cecilia currently?

A. 10
B. 12
C. 14
D. 16
E. 18

Hello generis, can you advice if my approach is correct

C = Cecilia
M = Mother

m=3c-2 <---- Two years ago, Cecilia's mother was three times as old as Cecilia
m=12+2c < ---- In 12 years, Cecilia's mother will be twice as old as Cecilia

How old is Cecilia currently? <--- C ?

3c-2 = 12+2c
3c-2c = 12+2
c= 14

Since two years ago, Cecilia's mother was three times as old as Cecilia - 2, so we add those two years to 14 and get 16 no ? I think I missed something though I answered correctly

dave13 , you're not missing anything. You did one step in your head (adding 2 at the end). I think that's what you're sensing.

You and kablayi (welcome!) used similar approaches with variables defined a bit differently.

You just didn't "remind" yourself explicitly -- as kablayi did by writing Cecilia's age "now" as "x + 2" -- that whatever you calculated for Cecilia's age would require you to add 2.

In short, good instincts!
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Re: Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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20 Jan 2018, 13:03
M = Cecilia's mother
C = Cecilia

Two years ago:
(M - 2) = 3(C - 2)
Simplifying the equation, M - 3C = -4 Equation 1

In twelve years:
(M + 12) = 2(C + 12)
Simplifying the equation, M - 2C = 12 Equation 2

Subtracting Equation 1 from Equation 2,
M - 2C = 12
- M - 3C = -4
C = 16. Hence Cecilia is currently 16 years old (Option D)
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Re: Two years ago, Cecilia's mother was three times as old as Cecilia. In  [#permalink]

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20 Jan 2018, 14:33
1
Current age of Cecilia = y and current age of Cecilia's mother = y

According to given statements :

x-2 = 3y & x+12 = 2(y+12)

Solving y =10
Re: Two years ago, Cecilia's mother was three times as old as Cecilia. In   [#permalink] 20 Jan 2018, 14:33
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