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# Jacob is now 12 years younger than Michael. If 9 years from now Micha

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 02:16
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3
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25% (medium)

Question Stats:

77% (01:34) correct 23% (02:02) wrong based on 136 sessions

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Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Kudos for a correct solution.

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Posts: 50009
Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 02:18
Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Kudos for a correct solution.

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Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 02:25
1
1
Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Kudos for a correct solution.

Jacob=x years, Mike=x+12 years
9 years from now,

2(x+9)=x+21
2x+18=x+21
x=3
x+4=7 years
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Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 03:19
1
Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Kudos for a correct solution.

J = M - 12
or J - M = -12 .... (1)
9 years from now..
(J + 9)*2 = M + 9
2J + 18 = M + 9
2J - M = -9 ..... (2)

Subtracting (1) from (2)

J = 3
This is Jacob's age today.

In 4 years, Jacob's age will be 7.

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Posts: 49
Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 03:56
1
[quote="Bunuel"]Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Jacob is now 12 years younger than Michael => J=M-12 - Eq1

If 9 years from now Michael will be twice as old as Jacob=> 2(J+9)=M+9 - Eq2

Substitute Eq1 in Eq2 to get 2(M-12+9)=M+9
Sp M=15 and J=3

how old will Jacob be in 4 years ?=>J+4=3+4=7
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Posts: 40
Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 11:55
1
Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Kudos for a correct solution.

Let age of Jacob be j years and Michael be m years

Present age as per given statement > j = m -12......... (1)

as per second given statement > m +9 = 2 (j + 9)

> m - 2j = 9........(2)

Solving for (1) and (2)

J = 3 , substitute the value in (1) you get M = 15.

SO age of jacob in four years = 3 + 4 = 7
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Posts: 132
Concentration: Strategy, Entrepreneurship
Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 12:02
2
Jacob is now 12 years younger than Michael
J=M-12------Equation 1

9 years from now Michael will be twice as old as Jacob
M= 2(J+9)----- Equation 2

by solving Equations 1 & 2 we get J =3

after 4 years Jacob will be 3+4=7 years

Ans is B

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Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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11 Sep 2015, 12:29
1
1
Jacob's present age = J
Michael's present age = M

"Jacob is now 12 years younger than Michael"

J = M - 12
M = J + 12---------------------------- (i)

"9 years from now Michael will be twice as old as Jacob"

M + 9 = 2(J + 9)

from (i) ,

(J +12) +9 = 2J + 18
J = 21 - 18 = 3

"how old will Jacob be in 4 years?"

J + 4 = 3 + 4 = 7

Option B.
Math Expert
Joined: 02 Sep 2009
Posts: 50009
Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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14 Sep 2015, 06:22
Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

Kudos for a correct solution.

KAPLAN OFFICIAL SOLUTION:

The first step to answering this question is translating the information in the problem into equations. If Jacob is 12 years younger than Michael, we can say that J = M – 12, where J is Jacob’s age and M is Michael’s age.

The second equation is a bit trickier to determine. You must keep in mind that it refers to the relationship between their ages in 9 years. Thus, Jacob will be J + 9 years old and Michael will be M + 9 years old. The equation we can then write if Michael will be twice as old as Jacob in 9 years is M + 9 = 2(J + 9).

Because the question wants us to solve for Jacob’s age in 4 years, we should next rewrite our first equation as M = J + 12. This allows us to substitute J + 12 for M in the second equation, which becomes (J + 12) + 9 = 2(J + 9). Then solve for J as follows:

J + 12 + 9 = 2(J + 9)

J + 21 = 2J + 18

3 = J.

However, you must remember that the question asks for Jacob’s age in 4 years. Since Jacob is 3 years old today, we know that he will be 7 years old in 4 years. Thus, the correct answer is choice (B).
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Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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14 Sep 2015, 10:35
Their age gap will never change, be it 9 years later or a 100 years later.

So 9 years from now, M - J = J, where J = 12. J's current age = 12-9 = 3. 4 years from now, he will be 7.

Cheers,
Sam
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Posts: 11
Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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20 Apr 2018, 03:28
M = M ---------------1 equation
J = M - 12. -----------2 equation
Then after 9 year M = M+9
J = M -12 + 9
2(M-3) = M+9
2M-6 = M+9
M=15....This is a Micheal age we need to find Jacob age, then put the value into second equation..you will get J=3
This is not final answer, we need to find next four year age of Jacob, so J = 3 + 4 = 7
So, J=7, this is our final answer!
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Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha  [#permalink]

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23 Apr 2018, 17:35
Bunuel wrote:
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3
(B) 7
(C) 15
(D) 21
(E) 25

We can let Jacob’s age today = j and Michael’s age today = m and create the equations:

j = m - 12

We know that 9 years from now, Michael will be (m + 9) years old, and Jacob will be (j+ 9) years old. At that time in the future, Michael will be twice Jacob’s age. Thus, we have:

m + 9 = 2(j + 9)

m + 9 = 2j + 18

m = 2j + 9

Substituting we have:

m = 2(m - 12) + 9

m = 2m - 24 + 9

15 = m

So j = 15 - 12 = 3.

So, in 4 years, Jacob will be 7.

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Re: Jacob is now 12 years younger than Michael. If 9 years from now Micha &nbs [#permalink] 23 Apr 2018, 17:35
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