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Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
10 Jan 2014, 01:57

Walkabout 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

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.

Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
09 Jun 2014, 14:32

Expert's post

Abraham00 wrote:

Bunuel wrote:

Walkabout 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.

Answer: D.

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).

Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
15 Jul 2014, 11:09

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.

Re: Jack is now 14 years older than Bill. If in 10 years Jack [#permalink]
14 Jun 2015, 16:28

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)

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