SOLUTION: Hello, please help me with this word problem I have no idea how to do it or where to get started. The directions say to solve using two variables. All I know is that you have to

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Question 264699: Hello, please help me with this word problem I have no idea how to do it or where to get started.
The directions say to solve using two variables. All I know is that you have to define the variables and show work.
The word problem:
Matrimburg had 8,000 residents. Of them, 1/6 of the females married 1/4 of the males. If no person in Matrimburg married more than once, how many of the town's residents were female?
please help, thanks for your time!
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the number of females. Let represent the number of males. Presuming that all 8000 residents are either male or female and there are no other unaccounted for possibilities, we can say:

Which we will find convenient later to express as:

Since no one married more than once, and presuming all of the marriages were the traditional two-person man/woman arrangements, one-sixth of the females must be equal in number to one-fourth of the males, that is:

Cross-multiplying, we obtain

Using the modified version of our first equation, make the substitution for , thus:

Now all you have to do is solve for

John

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
In order for 1/6 of the female residents
to marry 1/4 of the males, then 1/6 of the
female residents has to equal 1/4 of the males
because marriage is a one-to-one match.

Multiply both sides by
(1)
Also, I am given:
(2)
I can say this because all the residents
are either male or female
From (2),

Substitute this in (1)

and, from (2)

There are 4800 female residents and 3200 male residents
check:

Multiply both sides by

OK