So, how many people were in the office?!

[BringOnTheScience]

AQA..
1/4 of the women wear glasses.
3/8 of men wear glasses.
84 people in the office wear glasses altogether.
How many people were in the office?

DC1 and classmates couldn't solve it.
I can't see how without trial and error.

Any maths teachers?

84 is equal to 5/8, so you need to find out what 8/8 is.

I don't think it's 5/8, maybe 5/16

84x16/5 maybe

Are we assuming the same number of men and women there

I need a pen and paper

I don't think that is right.

1/4 of some number of women wear glasses - call this 1/4w
3/8 of some number of men wear glasses - call this 3/8m

All the people wearing glasses number 84, so that 1/4w + 3/8m = 84

I think you'd need to know what one of the terms was

You have to assume the same number of men and women I think

Surely unless you know the proportion of women to men you can't work it out

If it's equal numbers then it's easy. If you don't know the split it's impossible.

It's an equation with two unknowns. You can't solve it without another piece of information.

Not a teacher, but do have a maths degree.

I don't think that is solvable, so I think you have missed out a piece of information?

I tried to work this out. Got a figure of 252, and then scrolled down to the comments and realised how far off the mark my understanding is bloody maths...

Agree that you need to know ratio of men to women to work it out.

You can have equations with two unknowns. Apparently. m.wikihow.com/Solve-Systems-of-Algebraic-Equations-Containing-Two-Variables

I have got as far as x+1.5y=336 but that could be complete bollocks since the last time I did maths was AS Level 22 years ago.

Can't you just add up the fractions?

Disclaimer: I'm shit at maths. But I think if you add up the fractions it comes to a quarter of people on t he office (although I'm not convinced I know how to add up fractions) so the answer would be 84 x 4?

Sorry, no the fractions don't add up to a quarter. Told you I was shit at maths!

I got 268.8 which I don't think is right...

Do they add up to a third?

I don't think it can be 5/16 because that wouldn't give a whole number of people as the total.

Mind you neither does 5/8 but it couldn't be that anyway.

I've found someone asking this elsewhere online. The first line of the question is that there are twice as many women as men.

I got 134.40.... Oh dear

Aha. In that case it's trivial (mathematical term meaning it's been a long day and I can't be arsed).

So with chocs info we get

m=96, w=192, total = 288

84 people = 5/8.

However, 84/5 = 16.8 people

So 16.8 x 8 = 134.4 people.

Which is silly.