Question

2/3 of the men are married to 3/4 of the women in Fractionville. What fraction of the people in Fractionville are married?
I've gotten it to 2/3x = 3/4y but I'm not sure what to do from here.

Answer 1

you should have two equations, since you have two unknowns. so if you let x+y=1 you should be in good shape. (x and y are the corresponding fractions of the town that are male and female)

Answer 2

you need another equation
x+y=1
means the men and women add up to the total population

Answer 3

x = the number of men in fractionville and
y = the number of women in fractionville

Answer 4

how can x + y = 1 though?

Answer 5

if x is the fraction of the population that is male and y is the fraction of the town that is female, they should add up to 1 which is the fraction of people in the population

Answer 6

but how is x the fraction of- okay I kinda see, but explain how i get my x and y definitions?

Answer 7

@JunkieJim is correct

Answer 8

i just dont understand it though shouldnt
x + y = P (population)?

Answer 9

Yes, that's exactly what we're doing, only we're dividing everything by P so you've got \[\frac{x}{Population} +\frac{y}{Population} = \frac{Population}{Population}\] so that everything remains as fractions

Answer 10

Think of it this way: some fraction of the people are men and some fraction are women
so x+y=1
the fraction of the population that are married is 2/3 x (another fraction)

Answer 11

which of course is the same fraction as 3/4 y

Answer 12

I appreciate how you are taking the time to explain it to me. And I'm understanding it better. I can do the systems from here, but that x + y = 1 is bothering me

Answer 13

what you said makes sense Phi, I'm just wondering how i got my definitions for x and y

Answer 14

@mridrik: another way of looking at this is to call the total population p and the number of men m.
then, number of women = p - m
and you can write:\[\frac{2m}{3}=\frac{3(p-m)}{4}\]

Answer 15

your definitions should be modified
x = the fraction of the population that are men in fractionville and
y = the fraction of the population that are women in fractionville

Answer 16

so are my definitions wrong, or are they right but do not help me advance with the problem?

Answer 17

I would *not* use
x = the number of men in fractionville and
y = the number of women in fractionville

Answer 18

with asnaseers way, we get m = 9/17p, so how could I use that to get the answer?

Answer 19

2m/3 are married

Answer 20

you can only find m/p (a fraction)

Answer 21

so 2/3 * 9/17 gives us ?

Answer 22

now I'm confused again

Answer 23

the fraction married

Answer 24

but we already knew the fraction married 2/3

Answer 25

i have a feeling i sound pretty stupid right now to you guys

Answer 26

no - 2/3 is the fraction of men that are married - not the fraction of the population that are married.

Answer 27

double it (we have to count the women)

Answer 28

so 2/3 * 9/17 * 2?

Answer 29

Sounds good. we know 2/3 * 9/17 = 6/17 of the population is married men
3/4 * 8/17 is 6/17 of the population = married women
total fraction 12/17

Answer 30

You guys are genii! (I think thats genius plural)
Thank you, so 12/17 of the population of fractionville is married?

Answer 31

:) we've just had a bit more practice than you have mridrik thats all. and yes phi has the correct answer.

Answer 32

It makes me happy to know that people care about another's will to learn.

Answer 33

thats what makes this site so wonderful :)

Answer 34

If i could, i would make a program that gave each of you over 9000 medals

Answer 35

:O) - careful - we may drown in glory - lol!

Answer 36

yeah lol, my math teacher couldnt even get this today in class

Answer 37

try and be gentle on him - after all - he is also human :)

Answer 38

yes, maybe I'll get the chance to explain what you showed me to the class, even though i dont that well with public speaking, only about 20 students in my algebra 2 class

Answer 39

good luck my friend...

Answer 40

thanks for your help, have you ever heard of mathcounts?

Answer 41

no - what are they?

Answer 42

It's a program that my school participtes in with schools from around the United States, we go to regionals first, (district is too small) and usually win that, and then go to state where this one girl always wins, its from 6th to 8th grade (my last year) and its a blast when we go there to lexington this year (KY) but they questions get ridiculously hard towards the end of the competition and i bet you would beast them up

Answer 43

I'm sure as time goes by you will become a mathematical ninja and win that contest hands down :)
I'm probably far too old for that now :)

Answer 44

oh no way, the way you win is the top ten scorers in the written test get to go to a quick recall type thing, and she has won that in 6th grade and 7th grade, I got 40 something place and my friend got in the 30s, but there are a LOT of people there so thats pretty good i guess, our school got 10th place overall last year

Answer 45

that is an extremely good achievement. and never think that you will not be able to achieve even better goals for yourself - nothing in this world is impossible if you work hard enough at it. you certainly sound like someone who is willing to work hard to achieve high goals in life.

Answer 46

Thanks, I would like to be an engineer when I grow up, not really sure what they do, but everyone says it involves math so that sounds fun.

Answer 47

yes - there is a lot of maths involved in engineering. your main focus should be to do something you really enjoy - after all, you will most likely be working for the rest of your life in one particular job - so might as well pick something you really enjoy.

anyway - must go now. good talking to you.

Answer 48

you too