Maths puzzle

[clajen31]

(a + 4) / 10 = b

(a - 4) / 8 = b

find a

[Fibonacci]

a=36

(36+4) / 10 = 4
(36-4)/8=4

[WTW]

36

[clajen31]

By the way, I know the answer but was made to look a fool as I couldn't work it out in half a day - whilst at work doing other things. Interested how quick you clever lot answer!

[clajen31]

that was quick!

[clajen31]

I'm stupid

[clajen31]

Is this a well known puzzle or did you really just work it out?

[jno]

it's 3rd-form maths, rather than a puzzle... or it used to be when I was in the 3rd form many decades ago.

[JDOvengloves]

I got as far as b= 4 before you all beat me !

Simultaneous equations - if I remember right ( 30 years ago )

[Fibonacci]

worked it out
(a+4) / 10 = (a - 4)/8
so multiply out brackets
0.1a + 0.4 = 0.125a - 0.5
-0.1a from both sides
0.4 = 0.025a - 0.5
add 0.5 to both sides
0.9 = 0.025a
multiply both sides by 40
36 = 1a

[clajen31]

Then the midnight train is due in under the hour and I'm under it.

[WTW]

Or multiply a+4 by the 8, which equals a-4 multiplied by 10

8a+32 = 10a-40

2a = 72

a = 36

[jno]

WTW's way was the one I learnt. Of course numbers have all changed since then...

[clajen31]

it.

[THECORBYLOON]

10(A � 4) = 80B

8(A + 4) = 80B

Multiplying out shows

10A � 40 = 80B

8A + 32 = 80B

2A -72 = 0 so A must equal 36.