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# Jack is now 14 years older than Bill. If in 10 years Jack

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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

Set up the equations: [J = B + 14] and [J + 10 = 2(B + 10)], subtract the two and solve for B, this gives us B = 4.. From the first equation we know that Jack is 14 years older than Bill today, which means that Jack is 14 + 4 = 18 years old.. So naturally, in 5 years he's 23 years old.
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
Bunuel wrote:
Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

Currently: J = B + 14;
In 10 year: J + 10 = 2(B + 10);

Solving gives J = 18;

Thus in 5 years Jack will be 18 + 5 = 23 years old.

We know that J = B + 14

B = J + 14

So to add 10 to both sides, we get

J + 10 = 2 ( B + 14 ) + 10

Why should we have 2 ( B + 10 ) ?

Thanks,
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
Abraham00 wrote:
Bunuel wrote:
Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

Currently: J = B + 14;
In 10 year: J + 10 = 2(B + 10);

Solving gives J = 18;

Thus in 5 years Jack will be 18 + 5 = 23 years old.

We know that J = B + 14

B = J + 14

So to add 10 to both sides, we get

J + 10 = 2 ( B + 14 ) + 10

Why should we have 2 ( B + 10 ) ?

Thanks,

First of all, from J = B + 14, we get that B = J - 14, not B = J + 14.

Next, we are told that in 10 years Jack will be twice as old as Bill: in 10 years, Jack will J + 10 years and Bill will be B + 10 years. So, J + 10 = 2(B + 10).

Hope it's clear.
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
I did this using number substitution. When we set up J=B+14, and we want to know J+5, we can safely say we want B+19 here. Since B cannot be zero, a and b are ruled out. Then you substitute the remaining values, starting from the middle one, which is 23. And you get the answer.
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Interpreting the 2nd equation could get tricky.

I recommend using POE. It takes less than 1min.

b) 19 - 5 = Jack is 14 now and and therefore Bill is 0 years old. NEXT

c) 21 - 5 = Jack is 16 and Bill is 2. Then, in 10 years Jack will be 26 and Bill 12. That is not twice the age as stated, so move on to the next one.

d) 23 - 5 = 18 and Bill is 4. Then, in 10 years Jack will be 28 and Bill 14. CORRECT.
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
Thinking out the problem conceptually you can solve the problem quite quickly in your head(or paper):

1) If Jack is twice as old as Bill in 10 years then the difference between the two ages(at that time) is equal to Bill's age! Since they are 14 years apart (always), Bill is currently 4 and Jack 18.
2)18+5 = 23 -->(D)

No more than 30 seconds to solve this way
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

J+5 = ?
J = B + 14 => B = J - 14
J + 10 = 2 (B + 10) => J + 10 = 2B + 20 => J= 2B + 10
J = 2(J-14) + 10
J = 2J - 28 + 10
J = 2J -18
J = 18
=> 18 + 5
(A) 9
(B) 19
(C) 21
(D) 23
(E) 33
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

We first want to create variables for Jack’s age today and Bill’s age today.

J =Jack’s age today

B = Bill’s age today

Now we can use these variables to set up two equations.

We are given that Jack is now 14 years older than Bill. This relationship is represented in our first equation.

J = B + 14  Eq (1)

Next we are given that in 10 years Jack will be twice as old as Bill. Remember, in setting up this equation we must add 10 years to both Jack's and Bill’s current ages, respectively.

10 + J = 2(B + 10)

10 + J = 2B + 20

J = 2B + 10  Eq (2)

Now we can set our two equations (Eq (1) and Eq (2)) equal to each other and determine the value of B.

B + 14 = 2B + 10

B = 4

This means that Bill’s age today is 4.

Thus, we know that Jack’s age today is 14 + 4 = 18.

This means that Jack’s age in 5 years will be 18 + 5 = 23.

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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

currently
Bill = b
jack = b + 14

in 10 years

b + 14 + 10 = 2(b +10)
or b = 4

in 5 years jack will be
4 + 14 + 5 = 23

cheers through the kudos button if this helps
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

Here's a 2-variable solution:

PRESENTLY
Jack is now 14 years older than Bill.
Let B = Bill's present age
Let J = Jack's present age
So, we can write: J - B = 14

10 YEARS IN THE FUTURE
In 10 years, the both of them are 10 years older. So...
Let B + 10 = Bill's age in 10 years
So, J + 10 = Jack's age in 10 years

In 10 years Jack will be twice as old as Bill
So, to make their future ages EQUAL, we'll need to double Bill's age.
That is: (Jack's age in 10 years) = 2(Bill's age in 10 years)
So, we get: J + 10 = 2(B + 10)
Simplify: J + 10 = 2B + 20
Rearrange to get: J - 2B = 10

So, we now have 2 equations with 2 variables:
J - B = 14
J - 2B = 10

Subtract the bottom equation from the top equation to get: B = 4

So, Bill is PRESENTLY 4 years old.
This means that Jack is PRESENTLY 18 years old

How old will Jack be in 5 years?
Jack will be [spoiler]23[/spoiler] years old

Aside: Looks like the 1-variable solution is probably faster.

Cheers,
Brent
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Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9
(B) 19
(C) 21
(D) 23
(E) 33

Plugging in approach:

C) J+5 is 21, so J+10 is 26.
B+10 is 14 less than 26, so 12.
26/12 doesn't give us 2, NO
We can see that we need a bit higher number because 13 would be 26/13 = 2, and numerical answers are always listed in order of least to greatest so we should check D next.

D) J+5 is 23, so J+10 is 28.
J+10 is 14 less than 28, so 14.
28/14 = 2, YES.
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
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