Grandson's Home Workquestion.

[lordgyllene]

My 11 year old grandson recently started life at grammar school. This is his first maths homework question. I know you can get to the answer by trial and error but surely there is a mathematical/logical way to approach it. Parents and grandparents are stumped. Any suggestions?
There are five children in the house.
On each of the next six nights four of them go out.
No one child goes out on all six nights.
On the fjrst night the average age of the four is 38; second night 35; third night 36; fourth night 36; fifth night 38; sixth night 39.
What is the age pf the children?
Put us out of our misery please

[fiction-factory]

Well it would mess things up if one or more of them had a birthday during that 6 day period

[fiction-factory]

see whether he thinks 30, 34 ,42,46, 34 works.
Call them A, B, C, D, E

day 1 - ABCD
day 2 ABCE
day 3 ABDE
day 4 ACDE
day 5 ABDE
day 6 BCDE

this assumes I have not misread any of my scribbles

[lordgyllene]

sorry. should have said total age of the four etc...

[Togo]

I get the average age of the children as 9.22 years.
1 Take the total ages on the 6 nights ie 38, 35, 36,36,38,& 39 and divide it by the number of children who went out which is 4.
2 you now end up with the average ages of the children who went out on any given night, which gives you the figures 9.2,8.75,9,9,9.4 & 9.75
3 Add them up and you get 55.3 and divide by the number of nights which the children went out, which was 6.
4 55.3 divided by 6 is 9.22. The average age of the children was 9.22yrs old.

[fiction-factory]

I think the answer is more likely to be whole numbers (assuming no birthdays in this period) since decimal ages would change over the course of the week.
I don't think averages come into it now- it's just combinations of numbers that add up to the given totals

[fiction-factory]

What about ages of 7, 8, 10, 10* 11 (10 and 10* are the same age but the asterisk allows us to distinguish between two different boys)
Day 1- 7,10, 10*, 11 (38)
Day 2- 7,8,10,10* (35)
day 3- 7,8,10,11 (36)
day 4 - 7,8, 10*,11 (36)
day 5 - 7, 10, 10*, 11 (38)
day 6 - 8, 10, 10*, 11 (39)

[Prudie]

It's the average age though FF not the total age surely? So although they are described as children these people must be in their 30s/40s
Eg first night average age is 38
I've only just started to scribble but this seems very hard for an 11 year old??

[fiction-factory]

Yes, my first solution at 7:55 was done on that basis but then the OP apologised and said the question should read TOTAL rather than average. (Avoids a debate about arithmetic mean, geometric mean, median, mode)

[Prudie]

Of course! Missed that vital bit...

[Togo]

lordgyllene amended the op. 38,35 etc is the total age of the children who went out on any given night.

[Togo]

The single ages would have to be 7.8.9..11.12.
8,9,10,11=38
7,8,9,11=35
7,8,9,12=36
7,8,10,11=36
7,9,10,12=38
8,9,10,12=39

[Togo]

That should have read. 7,8,9,10,11,12

[Togo]

And the bottom list 7,9,11,12=39 So that no child goes out every night.

[lordgyllene]

Thanks for all your input. But I am still no nearer to discovering a mathematical formula to solve the question

[fiction-factory]

I don't think he is expected to use a formula. It looks as if here is more than one answer depending on whether you assume they are all different ages or some can be the same age. if we knew which people went on each day you could solve it by algebra (solving simultaneous equations) but we don't know the combinations for each day. So I felt the best approach was using trial and improvement. You could narrow down the range of numbers by noting that the mean of the ages would be 9-10 and that the difference between highest and lowest could only be small as the sums of any four all fell in the range 35-39.
Then just try some numbers and see if you make the 6 totals, and if it doesn't work just tweak some numbers until it works.
It's a good puzzle.

[fiction-factory]

It looks as if we have found 2 solutions. It's possible there are more.

[Togo]

Just a resume when I said that the average age of the children was 9.22 years, that was the average age of the children who went out.

[tamborine]

Ttal age =55.5

day 1 av age = 38 / 4 = 9.5av
2 = 35 / 4 = 8.75
3 = 36 / 4 = 9.00
4 = 36 / 4 = 9.00
5 = 38 / 4 = 9.5
6 = 39 / 4 = 9.75
Total 55.5

[fiction-factory]

The question isn't about averages though- the reference to average was a typo.
I'm not sure what that total in yours represents tambo.

[Old_Geezer]

After messing about on a spreadsheet for a while I came up with 7 8 10 10 11 too.

But I think it may change if you assume night 1 and night 5 are the same group, or night 3 and night 4.

I suspect there isn't enough information for a unique solution, but I've spent too much time on this one already to check.

IMO, unless how to get the required answer has been spelt out in class, this seems rather complex for an 11 year old. Unless it's a school for genii.