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?

Sorry, no, elephant. As Rafa points out, if less than half the men wear glasses and less than half the women wear glasses then less than half the total number of people in the office must wear glasses - so your total of 117 cannot be right. You needed to turn the "1/4 of women" into "x/yths of total office people" and you can't do that without the male:female ratio.

Perhaps the half a person is a monacle wearer

Just asked DS1 and he said it was the last question, so designed to split the 8/9s? He had a stab at it but got 144 not 288. Am hoping he grabbed some marks for working.

Last question - higher or foundation?
(Seems too easy to me to be the last question on a higher paper. Provided the DC actually read the whole question that is).

That can't be designed to split the 8/9s, surely?

I'd be quite surprised if yr 6s in schools using Singapore or Shanghai schemes couldn't have a reasonable go at that.

Obviously not using simultaneous equations. But with a barmodel and a good understanding of fractions it's doable.

higher or foundation

Higher.

Without the twice-as-many-women-as-men info there are multiple solutions - not quite an infinite number of solutions because you can't have a fraction of a person wearing glasses, but you can solve it with
w=12, m=216 (total 228)
w=24, m=208 (total 208)
And so for every multiple of 12 until
w=324, m=8 (total 336)

A total of 27 possible solutions - but with the info that there are twice as many women as men it becomes trivial.

Wow! Thank you all! :-)

DC1 and friends all apparently missed the extra ratio detail :-(

Perhaps a reminder to RTFQ for the rest of his exams is in order.

I agree that you have 5/8 and need to work out what 8/8 is

Sorry Hector you are wrong. If you RTTF you will see why.

(I am hoping that the people on this thread who can't do this question are not teachers, or are teacher of non STEM subjects or lower primary.)

Not a teacher, but since I do have special needs and also run a charity dealing mostly with special needs, I would love to hear if there are teachers who know ways to teach fractions easily. I have looked for fraction games and other manipulative, but what resources do you use? And how do you make the concept of fractions understandable?

I can do very basic math, but still by activity books and take time each week to practice. If I don't, I forget how to do even the basic things that I know. There is quite a good game that I found in a charity shop called ice cubeD, but I am always looking for ways to make STEM more accessible and easy.

These "equivalence cubes" are quite good Kitty. If you keep them on your desk and play with them then the idea of building fractions up and their percentage equivalent can get drilled in. Although if you have visual disability (am I thinking of the right poster?) then the equivalency labels wouldn't work for you unfortunately.

A more complex calculation like this one is a step further on though - it requires you to understand that a quarter of two thirds plus three eighths of one third equals seven twenty fourths and that understanding requires either natural ability or very good teaching - it's a top end GCSE question designed to identify the students with the highest ability. Those of us who are dashing it off in a minute are mostly mathematicians or similar, because MN threads saying "please help me with this maths question!" tend to attract mathematicians.

Thank you Time, and yes I am the right person. How big are the cubes? There might be some way to put a braille label on them or even raised tactile markings so if you have some vision, they may be usable.

I have sound number magnets that even come with addition subtraction multiplication and division signs which are pretty good

They should be big enough for some sort of Braille marking - they range in size from about a centimetre to two inches I think, and they're very brightly coloured. The markings aren't embossed on the version I have unfortunately. I'd happily post you mine, but you're a long way away aren't you?

I will PMU

Surely that wasn't the hardest question on the paper? Maths was my weakest subject at school, but it's a pretty straightforward question if you get fractions.

With the information provided (without the missing ratio of men to women), is it really that hard to answer by trial and error? Or am I being particularly obtuse? (More than possible!)
Find a number that's a multiple of 80 (closest simple number to the figure available). I started with 240. Try 80 as the total number of women, leaving 160 as the total number of men. This gives you 20 glasses wearing women and 60 glasses wearing men. 20 + 60 = 80. You need 4 more glasses wearing people to make 84. Make them women. 4 is one quarter of 16. Add this to the total of women wearing glasses: 96. Leaves you with 24 glasses wearing women out of a total of 96 (1/4) and 60 glasses wearing men out of a total of 160 (3/8), which means there are 256 people in the office altogether.

That's a solution heynonymous. But there are many others.
E.g. There are 3 glasses wearing women and 81 glasses wearing men in he office => 12 women in total and 216 men => 228 in the office.

The question didn't ask you for a possible solution, it asked you for a definitive number, which is impossible with the number of data points given.

That is not a top end GCSE question. Or at least if it is, the complaining about the new GCSE being too hard have been over exaggerated.