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Original poster

So, how many people were in the office?!

73 replies

BringOnTheScience · 25/05/2017 20:34

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?

OP posts:
Paperdove87 · 25/05/2017 21:02

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

Twice as many women as men so w=2m

0.25x2m + 3/8m = 84
4/8m + 3/8m = 84
7/8m = 84
M = 96
W = 192

TeenAndTween · 25/05/2017 21:03

cormorant Grin were you taught at the same place as I was?

CormorantDevouringTime · 25/05/2017 21:03

1/4 x 2 x m + 3/8 x m = 7/8 m = 84
=> m = 96
=> total number = 3 x 96 = 288

HarveySchlumpfenburger · 25/05/2017 21:03

If that's the first line of the question then it is much easier.

StealthPolarBear · 25/05/2017 21:03

Even if you can add them it's not 5/8

museumum · 25/05/2017 21:04

I was just about to say you need to know the men:women ratio. If the PP is right it's 2:1 so the question is quite easy.

W/4+3M/8=84
Sub M with 2W

W/4+6W/8=84
2w/8+6w/8=84
W=84
M=168

stjosephsbabyaspirin · 25/05/2017 21:04

I got as far as MaroonPencil. Then did just tried the easiest option - 8 men and 324 women works. Presumably there is a large number of options that would work?

chocoshopoholic · 25/05/2017 21:05

I get 288 people.

So, how many people were in the office?!
stjosephsbabyaspirin · 25/05/2017 21:08

Oh I missed the extra info

Bumpinthenight · 25/05/2017 21:10

1/4 = 2/8
2/8 + 3/8 = 5/8 = 84
1/8 = 84/5 which gives part of a person...

HarveySchlumpfenburger · 25/05/2017 21:11

288 is the answer I get too.

7/24 is equivalent to 84.

Agree stealth. There's no way more than half the people in the office could wear glasses if less than half the men and half the women do.

TeenAndTween · 25/05/2017 21:11

museumum No. w=2m not m=2w

Lynnm63 · 25/05/2017 21:19

AQA is this gcse? Just asked ds1 whose studying a level maths he says you'd need to know the ratio of men to women to answer the question then tried to explain it to me, something about simultaneous equations and how much I hated o level maths came flooding back.

prh47bridge · 25/05/2017 21:19

The question is from today's AQA Maths GCSE paper. As people have spotted, the OP has missed a line from the question. Chicchip88 has the correct first line. And TeenAndTween has the right answer.

BringOnTheScience - If your DC1 missed the first line it is not possible to answer the question. With the missing information...

w = 2m (where w is the number of women and m is the number of men)

women with glasses = 0.25w = 0.25(2m) = 0.5m

men with glasses = 0.375m

total with glasses = 0.5m + 0.375m = 0.875m (or seven eighths in real money)

0.875m = 84

therefore m = 96

therefore f = 192

therefore total in office = 96 + 192 = 288

prh47bridge · 25/05/2017 21:29

My son, who did the paper, tells me that the ratio was in the introduction to the question. The remainder of the facts were in a block below that. If you didn't read the introduction properly you would miss the ratio and wouldn't be able to solve the question.

hellokittymania · 25/05/2017 21:34

Can one of you who is good at math please so how to solve this? I have learning difficulties and find math extremely extremely difficult. But I'm interested in seeing how it's done.

TeenAndTween · 25/05/2017 21:44

hello a number of correct answers upthread with workings.

paperdove at 21:02 probably has it best explained.

basically you have to work out 2 equations from the information given which relate the men and the women.

the easier equation is w=2m (twice as many women as men)

so then in your first equation instead of writing 'w' you bung in '2m' instead.

TeenAndTween · 25/05/2017 21:45

(you have to be able to work with fractions and stuff as well though)

HarveySchlumpfenburger · 25/05/2017 21:49

Hello I used a bar model similar to the one choco has in her picture up thread. Although I've drawn the bar from the women underneath the one for the men.

hellokittymania · 25/05/2017 21:53

Tien, I somehow missed some pages. I have a lot of trouble with fractions actually.

HarveySchlumpfenburger · 25/05/2017 21:58

If you have a lot of trouble with fractions, then it will be a lot harder.

TeenAndTween · 25/05/2017 21:58

If you have trouble with fractions I think it might be quite hard to explain this question to you over a computer. It would be easier to have someone sitting next to you talking it through step by step.
Otherwise it would be like someone trying to explain a GCSE German comprehension exercise to me, when I know no German.

elephantoverthehill · 25/05/2017 22:00

I/4 +3/8 =84
5/8 = 84
1/8 = 10 1/2
3x 10.5 = 33
84 +33 = 117
I am not sure this correct at all but after the first 2 fractions it doesn't matter if they are male or female, it asks for the total number of people.

elephantoverthehill · 25/05/2017 22:04

Nooo 3x10.5 = another half a person!

TeenAndTween · 25/05/2017 22:05

elephant No.

You have assumed that there are equal men and women which isn't the case as was disclosed later down the thread. look at the answer at 21:02.

Also 3 x 10.5 = 31.5 not 33.