Tricky Questions

[no_ball]

Agreed, and in passing, we can do teaching, teachers can't do engineering...

[Guest55]

I am a qualified teacher though ... and, in passing, I could do Engineering as my Maths degree incuded fluid mechanics, quantum mechanics, relativity, vibrations and a large chunk of other Applied Maths!

[Guest55]

OP, can you please check the Magic square numbers you posted as they normally have consecutive numbers in them and 17 wouldn't fit with this?

[mystery]

No-ball, why did you say that Guest 55's method was illogical and that it involved a leap of faith? I don't follow. Both are OK methods using the same principle. G55's method is marginally quicker and probably will lead to them being able to answer other questions faster.

As for needing to explain it to the child, it shouldn't be difficult for a year 5 child should it?

[UmSusu]

Sorry, I seem to be missing something in G55's explanation: I do not see how the rulers have been subtracted when they are not the same in each line - in the first line there is one and in the second, 2 rulers.

[no_ball]

Guest55, i'll let you have the last word...oops.

Have a great day.

[no_ball]

Umsusu, I think it goes something like this from Guest55 method...

3 pencils and 1 ruler for 50p
2 pencils and 2 rulers for 56p, so easier to say that 1 pencil and 1 ruler is 28p.

This means the extra 2 pencils cost 22p ie 11p each..


So: if you subtract 1 pencil and 1 ruler from 3 pencils and 1 ruler, then one is left with 2 pencils and 50p-28p=22p.

so 1 pencil will be 11p.

[snoopy123]

Hi hope this helps with the number square.

The key is to start with the two lines where you have 2 numbers already.
This is the top horizontal. - 4 17 and the diagnol 5 - 17. As long as you choose numbers where these two add up to the same amount, the rest falls into place (and obviously for the diagnol this number needs to be 1 less than the horizontal).
What ever you choose, m ends up being six.
e.g. If I choose 8 for the horizontal then the diagnol needs to be 1 less 7 and you get the following.

8 4 17
16 7 6
5 18 6

Hope that makes sense

[xyzzy]

Umsusu, I think it goes something like this from Guest55 method...

3 pencils and 1 ruler for 50p
2 pencils and 2 rulers for 56p, so easier to say that 1 pencil and 1 ruler is 28p.

And it's an amusing example of two people in violent agreement talking past each other.

3x+y=50 (1)
2x+2y = 56 (2)

One of the protagonists eliminates x by multiplying (1) by 2:
6x+2y=100 (multiply by 2)
2x+2y=56

subtracting gives

4x=44
x = 11 (divide by 4)

Substituting back into (2) gives

22 + 2y = 56
2y = 34 (subtract 22 from each side)
y = 17 (divide through by 2)

The other protagonist eliminates x by dividing (2) by 2:

3x+y = 50
x + y = 28 (divide by 2)

subtracting:

2x = 22
x = 11 (divide by 2)

substituting back gives

11 + y = 28
y= 17 (subtract 11 from each side)

And from this they deduce things about engineers, fundamental principles, leaps of faith, etc, etc. The methods are almost identical, the steps gone through are almost identical, the only difference is that the second method saves one division by two.

[no_ball]

I know , its incredible. Well spotted, it took a few days...Here's to the next 'clash' of teacher versus engineer