 In the future equations venda Posers and Puzzles 03 Oct '16 10:32
1. 03 Oct '16 10:32
I get a mental block with the following type of problems you come across from time to time.
I'm not bothered about the answer but I would like to know how to form the necessary equations.
I get so far and then my mind goes into meltdown.
If someone could please give me the equations, I'll be able to see where I go wrong:-
5 people's ages a,b,c,d,e
a=a+b+c+d+e/5 -this is easy - 4a =b+c+d+e.
Now comes the awkward bits:-
when B= 3a , a+c = a+b+c+d+e
and d =3d (obviously 'cos if b is 3 times his age the other four must be as well)) and e =(2b +1)
All the 5 ages are <50
What are the five ages?
2. 03 Oct '16 22:561 edit
scratch that, too many beers.
3. 04 Oct '16 00:33
Originally posted by venda
Now comes the awkward bits:-
when B= 3a , a+c = a+b+c+d+e
and d =3d (obviously 'cos if b is 3 times his age the other four must be as well)
and e =(2b +1)
All the 5 ages are <50
What are the five ages?
At least two equations make no sense:

a+c = a+b+c+d+e

d =3d
4. 04 Oct '16 01:07
Originally posted by HandyAndy
At least two equations make no sense:

a+c = a+b+c+d+e

d =3d
....Thats what I was thinking. No wonder why his head is exploding
5. 04 Oct '16 07:48
Originally posted by joe shmo
....Thats what I was thinking. No wonder why his head is exploding
O.k.Maybe I've mis-interpreted the thing.
I'll type it in as it appears in the newspaper:-
"Five men of different ages under 50 are celebrating their joint birthdays.
Alan's age is the average of their 5 ages.
When Bob is 3 times Alan's age today, the sum of Alan and Colin's ages will be equal to the sum of their 5 ages today.
Furthermore, Derek will be 3 times his age today and Eric will be one year more than double Bob's age today.
Who is the youngest and how old is he?
Good luck and thanks in advance.
6. 05 Oct '16 00:451 edit
Originally posted by venda
O.k.Maybe I've mis-interpreted the thing.
I'll type it in as it appears in the newspaper:-
"Five men of different ages under 50 are celebrating their joint birthdays.
Alan's age is the average of their 5 ages.
When Bob is 3 times Alan's age today, the sum of Alan and Colin's ages will be equal to the sum of their 5 ages today.
Furthermore, Derek will be 3 ...[text shortened]... ouble Bob's age today.
Who is the youngest and how old is he?
Good luck and thanks in advance.
Seems like a lot of unknowns in to little equations to me. Maybe your notation was just off a bit.

Let a,b,c,d,e equal their current ages; let A,B,C,D,E equal their future ages.

a = (a + b + c + d + e) / 5

a = ( b + c + d + e ) / 4 1 equation-4 unknowns

At the time of the next set of equations:

B = 3a

A + C = a + b + c + d + e

D = 3d

E = 2b + 1

That is the system as far as I can see. It doesnt lok like a straight forward substitution to me...but have at it.
7. 05 Oct '16 02:42
Originally posted by venda
O.k.Maybe I've mis-interpreted the thing.
I'll type it in as it appears in the newspaper:-
"Five men of different ages under 50 are celebrating their joint birthdays.
Alan's age is the average of their 5 ages.
When Bob is 3 times Alan's age today, the sum of Alan and Colin's ages will be equal to the sum of their 5 ages today.
Furthermore, Derek will be 3 ...[text shortened]... ouble Bob's age today.
Who is the youngest and how old is he?
Good luck and thanks in advance.
a = (a+b+c+d+e)/5

5a = a+b+c+d+e

4a = b+c+d+e
--------
B = 3a

b+y = 3a

y = 3a-b
--------
A+C = a+b+c+d+e

a+y+c+y = a+b+c+d+e

2y = b+d+e

y = (b+d+e)/2
--------
D = 3d

d+y = 3d

y = 2d
--------
E = 1+2b

e+y = 1+2b

y = 1+2b-e
--------
y = 3a-b

y = (b+d+e)/2

y = 2d

y = 1+2b-e

4a = b+c+d+e
-------
(b+d+e)/2 = 2d

b+d+e = 4d

b+e = 3d
-------
2d = 1+2b-e

2d = 1+(b+e)+b-2e

2d = 1+3d+b-2e

2e = 1+d+b

2e = 1+b+(b+e)/3

6e = 3+3b+b+e

5e = 3+4b

idk
8. 05 Oct '16 07:58
Presume idk means I don't know.
Looks to me like you have to assume a value for 1 unknown and then see if the equations work.
Anyway, thanks to you both.
The answers will be in next weeks Sunday times so I'll plug in the numbers and see if the equations work.
In the meantime I might have another look and see if substitution is in fact possible.
9. 05 Oct '16 13:20
Originally posted by HandyAndy
At least two equations make no sense:

a+c = a+b+c+d+e

true for b+d+e=0

d =3d
true for d=0
10. 05 Oct '16 19:01
Originally posted by Ponderable
true for b+d+e=0

d =3d true for d=0
The equations make no sense in the context of the puzzle.

Do you think three of the men are zero years old?
11. 07 Oct '16 16:56
Originally posted by venda
I get a mental block with the following type of problems you come across from time to time.
I'm not bothered about the answer but I would like to know how to form the necessary equations.
I get so far and then my mind goes into meltdown.
If someone could please give me the equations, I'll be able to see where I go wrong:-
5 people's ages a,b,c,d,e
a=a+b+ ...[text shortened]... four must be as well)) [b] and
e =(2b +1)
All the 5 ages are <50
What are the five ages?[/b]
If d =3d is not a typo, d=0 (a newborn)
12. 07 Oct '16 19:03
Originally posted by JS357
If d =3d is not a typo, d=0 (a newborn)
It's not a typo the relevant text from the puzzle is:-
When Bob is 3 times Alan's age today, the sum of Alan and Colin's ages will be equal to the sum of their 5 ages today.
Furthermore, Derek will be 3 times his age today.
But it's true that d does not equal 3d.
The two unknowns are different
13. 07 Oct '16 21:231 edit
Originally posted by venda
It's not a typo the relevant text from the puzzle is:-
When Bob is 3 times Alan's age today, the sum of Alan and Colin's ages will be equal to the sum of their 5 ages today.
Furthermore, Derek will be 3 times his age today.
But it's true that d does not equal 3d.
The two unknowns are different
Surely you need

d + x = 3d, where x is the 'in a the future'

So x = 2d, which should reduce the variables. . , the number of years in the future is 2 x D's present age

I think someone else had that earlier?
14. 07 Oct '16 21:54
Originally posted by JS357
If d =3d is not a typo, d=0 (a newborn)
Surely = you jest
15. 07 Oct '16 23:35
Originally posted by venda
O.k.Maybe I've mis-interpreted the thing.
I'll type it in as it appears in the newspaper:-
"Five men of different ages under 50 are celebrating their joint birthdays.
Alan's age is the average of their 5 ages.
When Bob is 3 times Alan's age today, the sum of Alan and Colin's ages will be equal to the sum of their 5 ages today.
Furthermore, Derek will be 3 ...[text shortened]... ouble Bob's age today.
Who is the youngest and how old is he?
Good luck and thanks in advance.
Derek will be 3 times his age today

Three times whose age?