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?

[CremeEggThief]

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

[StealthPolarBear]

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

[StealthPolarBear]

84x16/5 maybe

[StealthPolarBear]

Are we assuming the same number of men and women there

[StealthPolarBear]

I need a pen and paper

[UncontrolledImmigrant]

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

[StealthPolarBear]

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

[GreyVelvet]

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

[CormorantDevouringTime]

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

[DarkFloodRises]

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

[TeenAndTween]

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?

[GinGeum]

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...

[TheUnseenAcademic]

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

[MaroonPencil]

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

[MaroonPencil]

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.

[ClashCityRocker]

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?

[ClashCityRocker]

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

[SpuriouserAndSpuriouser]

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

[ClashCityRocker]

Do they add up to a third?

[HarveySchlumpfenburger]

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.

[Chocchip88]

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

[ClashCityRocker]

I got 134.40.... Oh dear

[CormorantDevouringTime]

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

[TeenAndTween]

So with chocs info we get

m=96, w=192, total = 288

[Gingernaut]

84 people = 5/8.

However, 84/5 = 16.8 people

So 16.8 x 8 = 134.4 people.

Which is silly.