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A Math Problem  
User currently offlineJuanr From , joined Dec 1969, posts, RR:
Posted (9 years 8 months 1 day 3 hours ago) and read 1214 times:

This is a simple math problem that my cousin asked me to solve and I must admit I have not been able to. (law is killing my math abilities)  Sad

This is it:

My age now is two times (the double) of the age that you had when I had your age. When you'll have my age, our ages combinated will be 63. How old are we?

This is not for any class or contest so there is no hurry, I'll keep trying myself.

Juan
SKBO

27 replies: All unread, showing first 25:
 
User currently offlineEGGD From United Kingdom, joined Feb 2001, 12443 posts, RR: 35
Reply 1, posted (9 years 8 months 1 day 3 hours ago) and read 1208 times:

The reason why you're having so much trouble with it is because its badly worded, its quite a simple problem and if it was worded correctly i'm sure you'd get it quickly!

User currently offlineJuanr From , joined Dec 1969, posts, RR:
Reply 2, posted (9 years 8 months 1 day 3 hours ago) and read 1198 times:

EGGD

It is perfectly worded, I asked before posting.

Juan
SKBO


User currently offlineEGGD From United Kingdom, joined Feb 2001, 12443 posts, RR: 35
Reply 3, posted (9 years 8 months 1 day 3 hours ago) and read 1194 times:

Well, don't try and do it in your head, write everything down and work through it logically.

User currently offlineJuanr From , joined Dec 1969, posts, RR:
Reply 4, posted (9 years 8 months 1 day 3 hours ago) and read 1187 times:

I am not trying I already have three A4 size sheets filled with ecuations on both sides, I had not post this if I haven't been trying this for hours.

Juan
SKBO


User currently offlineEGGD From United Kingdom, joined Feb 2001, 12443 posts, RR: 35
Reply 5, posted (9 years 8 months 1 day 3 hours ago) and read 1184 times:

wow, hours? Maybe you should just give up!  Big grin

User currently offlineJuanr From , joined Dec 1969, posts, RR:
Reply 6, posted (9 years 8 months 1 day 2 hours ago) and read 1173 times:

EGGD:

I never give up

Juan
SKBO


User currently offlineCanuckpaxguy From , joined Dec 1969, posts, RR:
Reply 7, posted (9 years 8 months 1 day 2 hours ago) and read 1161 times:

Ages are 21 and 42.
Am I missing a trick here?

Oh wait - I misred the question....gimmie a sec.
I must have "combinated" the numbers wrong.

G

[Edited 2004-12-01 00:05:17]

User currently offlineThecoz From , joined Dec 1969, posts, RR:
Reply 8, posted (9 years 8 months 1 day 2 hours ago) and read 1159 times:

2x + x = 63

3x = 63

x = 21

You are 42 yrs (2x)

The other is 21 yrs (x)

 Smile


User currently offlineArniepie From Belgium, joined Aug 2005, 1265 posts, RR: 1
Reply 9, posted (9 years 8 months 1 day 2 hours ago) and read 1156 times:

25.2 years old and 12.6 years old



[edit post]
User currently offlineEGGD From United Kingdom, joined Feb 2001, 12443 posts, RR: 35
Reply 10, posted (9 years 8 months 1 day 2 hours ago) and read 1154 times:

No! As I said, it was worded really badly..

You should have let him work it out though, especially after all this time!  Big grin


User currently offlineThecoz From , joined Dec 1969, posts, RR:
Reply 11, posted (9 years 8 months 1 day 2 hours ago) and read 1127 times:

it looks like more of a word problem to me.

User currently offlineJuanr From , joined Dec 1969, posts, RR:
Reply 12, posted (9 years 8 months 1 day 2 hours ago) and read 1127 times:

No, I already came to those answers and they did not fit in, if the age of "I" is 2Y, then Y is not the current age of "YOU" 2Y is the age "YOU" had when "I" had the age "YOU" has now, so those answers in which "I" age is the double of "YOU" are wrong. Also, notice that 63 is not the current combinated age of both "I" and "YOU", it is the combinated age when "YOU" gets the age that "I" now has.

EGGD: it is perfectly written but If you have doubts then I'll post the original question in Spanish and see if you can write it down in english better, that would be more useful than keep on bashing.:

"La edad que yo tengo es el doble de la edad que tu tenías cuando yo tenía tu edad. Cuando tu tengas la edad que yo tengo, la suma de nuestras edades será 63. Qué edades tenemos tu y yo?

Juan
SKBO


User currently offlineArniepie From Belgium, joined Aug 2005, 1265 posts, RR: 1
Reply 13, posted (9 years 8 months 1 day 2 hours ago) and read 1119 times:

EGGD,

Sorry, couldn't help myself.

To make things up with you I'll give U another one, just logics and no real maths but a nice one anyway.


5 pirates on a ship have a 100 bars of gold.
Being pirates ,they want to share as little as possible.
All the pirates have a different age and the oldest pirate can make the first suggestion about splitting up the bars.
If a majority doesn't agree with the proposed deal they may shoot the oldest pirate , then the next in line (2nd oldest) can make a suggestion, and so on.

What does the oldest pirate propose so he can keep his life and also keep as many bars as possible for himself.

keep in mind that all pirates act logically and no emotions are involved.



[edit post]
User currently offlineEGGD From United Kingdom, joined Feb 2001, 12443 posts, RR: 35
Reply 14, posted (9 years 8 months 1 day 2 hours ago) and read 1105 times:

Juan - Firstly, there is no such word as 'combinated'. Secondly, there is no insinuation in the question as to whether it is all 3 ages combined or merely the concurrent ages. Although, the way the second sentence is constructed suggests that it is the latter and hence people come to the conclusion that the two ages are 42 and 21. For all intents and purposes, both answers are correct (unless i've skipped something huge!  Big grin).

User currently offlineArniepie From Belgium, joined Aug 2005, 1265 posts, RR: 1
Reply 15, posted (9 years 8 months 1 day 1 hour ago) and read 1082 times:

Juan - Firstly, there is no such word as 'combinated'. Secondly, there is no insinuation in the question as to whether it is all 3 ages combined or merely the concurrent ages. Although, the way the second sentence is constructed suggests that it is the latter and hence people come to the conclusion that the two ages are 42 and 21. For all intents and purposes, both answers are correct (unless i've skipped something huge! ).

Actually the answer is never 21 and 42.
Juanr is specifically asking for the ages at the present time, the combined (iso combinated) age of 63 refers to an age in the future (When you'll have my age)

So to conclude

juanr's Cousin (=person A) age NOW is 2 times (=2x) the age of Juanr (=person B)
When B has the present age of A his age will be 2x, at the same moment A's age will be 2x + x ,he will have aged exactly x-years (the same as person B)
So at 63 their combined age will be 2x(=A)+2x+x(=B)=63
5x=63
x=12.6 (present age B)
2x=25.2 (present age A)




[edit post]
User currently offlineVirginFlyer From New Zealand, joined Sep 2000, 4537 posts, RR: 41
Reply 16, posted (9 years 8 months 1 day 1 hour ago) and read 1067 times:

I don't believe we have had the correct answer yet.

'My age' = 42; 'Your age' = 21 doesn't satisfy the final requirement: When you'll have my age, our ages combinated will be 63. In this case, when you are 42, I am 63, so the combined age is 105.

'My age' = 25.2; 'Your age' = 12.6 doesn't satisfy the first requirement: My age now is two times (the double) of the age that you had when I had your age. In this case, when I was your age (12.6), you were 0. Double of 0 is still 0.

The best way to do this is to write equations, and make sure they match up with exactly what is being said. Before writing equations, we should define some variables, noting that there are three time instants being specified - the past (the age that you had when I had your age), the present (the ages we are looking for) and the future (When you'll have my age). Here are the variables:

An = my age now
Ap = my age past
Af = my age future

Bn = your age now
Bp = your age past
Bf = your age future

Da = Age diffence between you and I.

All of these numbers should have a single solution if this is a sensible problem.

Now we take the first statement:

My age now is two times (the double) of the age that you had when I had your age

We express this as:

An = 2Bp

Now, because this occurs at a time when i was your present age, it was Da years ago. I.e. Bp = Bn - Da

An = 2(Bn - Da)

But we know that Bn = An - Da (because Da is the age difference)

An = 2((An - Da) - Da)

An = 2(An - 2Da)

An = 2An - 4Da

An = 4Da


This is a key equation.

Now, we look at the second statement:

When you'll have my age, our ages combinated will be 63

We express this as:

Af + Bf = 63

Because this occurs at a time when you are my present age, it is Da years in the future. I.e. Af = An + Da, Bf = An

An + Da + An = 63

2An + Da = 63


Now recalling the key equation An = 4Da

8Da + Da = 63

9Da = 63

Da = 63/9

Da = 7


We are now able to solve:

An = 4Da

An = 4 x 7

An = 28

Bn = An - Da

Bn = 28 - 7

Bn = 21


We should now check that this agrees with the statements:

My age now is two times (the double) of the age that you had when I had your age

When I was 21, you were 14. 28 is two times 14. Condition Satisfied

When you'll have my age, our ages combinated will be 63

When you are 28, I will be 35. 28 + 35 is 63. Condition Satisfied

Thus the answer to the problem is:

'My age' = 28, 'Your age' = 21

V/F

[Edited 2004-12-01 01:33:58]


"So powerful is the light of unity that it can illuminate the whole earth." - Bahá'u'lláh
User currently offlineYooYoo From Canada, joined Nov 2003, 6057 posts, RR: 51
Reply 17, posted (9 years 8 months 1 day 1 hour ago) and read 1064 times:

The answer is C...always go for C.


Andreas  Big thumbs up



I am so smart, i am so smart... S-M-R-T... i mean S-M-A-R-T
User currently offlineDamirc From Slovenia, joined Feb 2004, 724 posts, RR: 7
Reply 18, posted (9 years 8 months 1 day ago) and read 1022 times:

Arniepie ...

... well ... one solution would be (to keep the majority of votes) to keep 33 bars, and give 33 bars to the 2nd and the 3rd oldest pirate and the remaining gold bar to the 4th oldest pirate. The youngest pirate stays empty handed, but the majority would presumably accept such a solution.

What's your solution?  Smile

D.


User currently offlineZKSUJ From New Zealand, joined May 2004, 7086 posts, RR: 12
Reply 19, posted (9 years 8 months 16 hours ago) and read 980 times:

It sounds like a case of Simutaneous Equations.

User currently offlineJuanr From , joined Dec 1969, posts, RR:
Reply 20, posted (9 years 8 months 11 hours ago) and read 953 times:

VirginFlyers: Thank You Very Much!!! That is the right answer; I'll check the procedure later carefully in order to see where I was wrong.

My cousin is very happy about it.

Welcome to my RU list.

Juan
SKBO


User currently offlineGdabski From Poland, joined Oct 2001, 423 posts, RR: 0
Reply 21, posted (9 years 8 months 8 hours ago) and read 925 times:

Alternatively, to use less symbols, you can solve these simultaneous equations:

x - my current age
y - your current age
(x-y) - age difference now, time from when I had your age to present, time from present to when you'll have my age

My age now is two times of the age that you had when I had your age
x=2(y-(x-y))

When you'll have my age (be x years old) our ages combinated will be 63
x+(x+(x-y))=63

/Gdabski

[Edited 2004-12-01 18:35:44]

User currently offlineJfkaua From United States of America, joined Aug 2004, 1000 posts, RR: 3
Reply 22, posted (9 years 8 months 5 hours ago) and read 881 times:

ah we learned this freshman year at my school.. i owned at these things.. i did it similar to the way Gdabski does it
-----
on the pirate question.. when they vote, does the oldest count?

[Edited 2004-12-01 21:52:59]

User currently offlineArniepie From Belgium, joined Aug 2005, 1265 posts, RR: 1
Reply 23, posted (9 years 8 months 2 hours ago) and read 847 times:

on the pirate question.. when they vote, does the oldest count?


All votes count offcourse.

Damirc,

Sorry it is not that easy.


[Edited 2004-12-02 00:42:52]


[edit post]
User currently offlineDamirc From Slovenia, joined Feb 2004, 724 posts, RR: 7
Reply 24, posted (9 years 7 months 4 weeks 1 day 2 hours ago) and read 804 times:

Okay. I gave that pirate puzzle some more thought.

So let's go from the opposite end.

If only Pirate 5 is alive: he gets all the 100 bars - therefore he will only vote yes if he is given all of the 100 bars.

If Pirates 4 and 5 are alive: he will never win the majority with Pirate 5 since P5 can get a better deal in any case. Therefore Pirate 4 can maximally get 0 bars (in any case).

If Pirates 3, 4 and 5 are alive: P3 will take 50, P4 will take 50 (both will vote yes), and P5 will get 0.

P2, P3, P4 and P5 are alive: they need a majority vote therefore P2, P3 and P4 must vote yes (we already know that P5 will always vote with a no) - P4 will vote no if he gets less than 50 bars, since he can get 50 bars if he lets P2 die and splits the bounty with P3. P3 will do the same. Therefore P2 would get 0, P3 - 50 and P4 - 50, P5 - 0 (P2 will get to keep his life).

P1, P2, P3, P4 and P5 are alive: P1's priority is his life (requirement) and if he gets any goldbars, he'll be happy. P2 will be happy if he gets more than 0 bars. P3 or P4 will only vote yes if they get at least 50 bars. Therefore (if my assumptions are correct thus far):

P1 takes 48 bars and keeps his life. - He obviously votes yes.
P2 gets 1 bar (he's better off than if P1 dies). He votes yes.
P3 gets 51 bars (he's better off than if P1 and P2 die). He votes yes.
P4 gets 0 bars. He votes no.
P5 gets 0 bars. He votes no.

We have 3 yes votes and 2 no votes - the majority acceps the solution, and P1 keeps his life.

Arniepie: any better now?  Big grin

D.


25 Post contains images FutureUApilot : Wow, with all the BN's and AF's and such, I'm surprised I didn't see all that many Airline abbreviations... -Sam
26 HAWK21M : 42 & 21. regds MEL
27 USAFHummer : Wow...good work VF!! Now why do I have a sudden urge to take a remedial math course? Greg
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