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Age Problems OG 153

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by HPengineer » Sun Aug 01, 2010 7:23 pm
153 Problem solving from OG 12th edition.

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?


What i did was build an age chart but something is going drastically wrong. Can some one help me out?

Now
Jack = B + 14
Bill = B

5 years
Jack = B + 19
Bill = B + 5

10 years
Jack = B +24
Bill = B + 10

Is there something wrong with my age chart?
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by selango » Sun Aug 01, 2010 7:35 pm
J=B+14

after 10yrs,

J+10=2(B+10)

J+10=2B+20

J-2B=10

J-B=14

B=4,J=18

Jack current age=18

In 5 yrs Jack age =23 yrs
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by Rahul@gurome » Sun Aug 01, 2010 7:35 pm
Now
Jack = B + 14
Bill = B

5 years
Jack = B + 19
Bill = B + 5

10 years
Jack = B +24
Bill = B + 10

So 2*(B + 10) = B + 24
Or 2B + 20 = B + 24.
Or B = 4

So Jack's age in 5 years is 4+ 19 = 23.

Your chart is correct
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by HPengineer » Sun Aug 01, 2010 7:38 pm
Thanks!!!! I always make silly mistakes I was plugging the 4 into the equation B+14......

Very very comforting to know my chart was correct.

Cheers
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by helenec » Sun Aug 01, 2010 7:40 pm
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?

now: J = B + 14

in 5 years: there is no info regarding the age relations

in 10 years: J + 10 = 2*(B+10) (Jack will be twice as old as Bill)

if you combine the info now + in 10 years you get:

B + 14 = 2*(B+10) - 10
B+14 = 2B+20-10
B = 4

J = 14 + 4 = 18

in 5 years Jack will be 23

hope it helps :-)
Last edited by helenec on Sun Aug 01, 2010 7:42 pm, edited 1 time in total.
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by selango » Sun Aug 01, 2010 7:42 pm
Let the current age of Jack be J and Bill be B.

J = B + 14
This is correct..

After 10 years both ages increased by 10.It should be calculated from current age
J+10=2(B+10)

J-2B=10

Calculating bot equations we get J=18,B=4 which is current age.

After 5 yrs both age increased by 5..
J+5=18+5=23

Hope this clarify..
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by Ian Stewart » Mon Aug 02, 2010 12:02 am
You don't actually need any algebra here. If Jack is now 14 years older than Bill, Jack is always going to be 14 years older than Bill. So when Jack is twice as old as Bill, Jack is 28 and Bill is 14. We know that's the situation in ten years; in five years Jack is 23 and Bill is 9.
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by kvcpk » Mon Aug 02, 2010 12:13 am
Ian Stewart wrote:You don't actually need any algebra here. If Jack is now 14 years older than Bill, Jack is always going to be 14 years older than Bill. So when Jack is twice as old as Bill, Jack is 28 and Bill is 14. We know that's the situation in ten years; in five years Jack is 23 and Bill is 9.
Thats Awesome approach.. Thanks Ian.
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by selango » Mon Aug 02, 2010 12:54 am
Excellent Ian......
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by tryreallyhard » Sat Jun 18, 2011 3:47 pm
Though I am not mathematically challenged, I made a mistake with this type of word questions. It's been a while since I solve word problems. I don't think they are difficult, but our brains have been occupied with other things.

I find the following explanation at https://www.oojih.com/show/wordproblem/age/ is helpful to jog my memory. The other study guides on work rate is particularly helpful for me.
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by MBA.Aspirant » Sat Jun 18, 2011 4:09 pm
HPengineer wrote:153 Problem solving from OG 12th edition.

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?


What i did was build an age chart but something is going drastically wrong. Can some one help me out?

Now
Jack = B + 14
Bill = B

5 years
Jack = B + 19
Bill = B + 5

10 years
Jack = B +24
Bill = B + 10

Is there something wrong with my age chart?
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=B+14
J+10 = 2(B+10)=2b+20
J= 2b+10

B+14=2b+10
B=4

J= 4+14 = 18 now

J in 5 years = 18+5 = 23
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by GMATGuruNY » Sun Jun 19, 2011 1:33 am
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 can plug in the answers, which represent Jack's age in 5 years.

Answer choice C: 21
Jack now is 21-5 = 16.
Bill now is 16-14 = 2.
Jack in 10 years = 16+10 = 26.
Bill in 10 years = 2+10 = 12.
To be twice as old as Bill in 10 years, Jack's age needs to increase just a bit.
Answer choice D will increase both ages by 2 years -- Jack will be 26+2 = 28 and Bill will be 12+2 = 14 -- making Jack twice as old.

The correct answer is D.

To determine the correct answer, we had to plug in only one answer choice, a very efficient way to solve.
Another advantage: it is virtually impossible to answer incorrectly when we plug in the answers.
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by theldot » Sun Jan 01, 2012 1:50 pm
Okay, I was doing this problem and was trying to work with only one variable. Is it possible to do? I got the following:

Jack = B +14
Bill = B

In 10 Years:
Jack = 2(B+10)
Bill = B+10

The equations aren't working when I'm trying this... can someone please tell me if this is possible with using one variable? I'm not seeing where J+10 comes from if using two variables.
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by chieftang » Sun Jan 01, 2012 2:15 pm
theldot wrote:Okay, I was doing this problem and was trying to work with only one variable. Is it possible to do? I got the following:

Jack = B +14
Bill = B

In 10 Years:
Jack = 2(B+10)
Bill = B+10

The equations aren't working when I'm trying this... can someone please tell me if this is possible with using one variable? I'm not seeing where J+10 comes from if using two variables.
With two unknown quantities, start with two variables. Sometimes one variable might drop out, or else you can solve a system of two simple linear equations. And when setting these up with two variables, try this approach: ALWAYS assign a variable to the quantity you're trying to determine

What are you trying to determine here? Answer: Jack's age 5 years from now.
So, let J = Jack's age 5 years from now.
Then J-5 = Jack's age today.

What other quantities are there in this problem? Answer: Bill's age today.
So, let B = Bill's age today.

How do these quantities interact with each other? Answer:
1. J-5 = B+14 (Jack is now 14 years older than Bill)
2. J-5+10 = 2(B+10) (Jack will be twice Bill's age in 10 years)

Rearrange eqn #1:
B = J-19
Substitute this in to eqn #2:
J-5+10 = 2(J-19+10)
Solve for J:
J=23

5 years from now, Jack will be 23 years old.
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by theldot » Sun Jan 01, 2012 4:55 pm
Wait, sorry for reviving this. Rahul@gurome explains how to do this with just variable B - this makes sense now. I'm having trouble with this word equations. Anyone have any drills for this stuff besides the OG?
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