Math Forum Discussions

josh rappaport

Posts: 7
Registered: 12/6/04

Re: algebra
Posted: Nov 1, 1997 1:52 AM

Plain Text

Dear Liz,

Here's one way you can do this problem.

Start with the Senate, since you know the total number of senators, which
is 100.

Start by noting the obvious:
Male senators + female senators = 100 (Equation 1)
or, abbreviating: MS + FS = 100 (Equation 2)

Then, given that the ratio of male to female senators is 19:1, you can set
up the proportion:
Male senators:female senators::19:1
again, abbreviating: MS:FS::19:1

Cross-multiplying, you get:
MS = 19 FS (Equation 3)

Substituting this value of MS into Equation 1, you get:
19FS + FS = 100

Using simple algebra, you find that FS, the number of female senators, is 5.
Since the total number of senators is 100, the number of male senators is 95.

So far you have:
FS = 5 and MS = 95

Now turn your attention to the House of Representatives.
Since you know that the ratio of men to women in the house is 4:1,
you can set up this proportion:
MH:WH::4:1

Cross-multiplying here, you get:
MH = 4WH (Equation 4)

Now look at this statement from the problem:
"The Senate and the House together have a ratio of men to women of 5:1"

This could be translated as:
(MS + MH):(WS + WH):5:1

But substituting the actual values you found for MS and WS, you get:
(95 + MH):(5 + WH):5:1

Cross-multiplying again, you get:
95 + MH = 25 + 5WH

Then substituting the value for MH from Equation 4, this becomes:
95 + 4WH = 25 + 5WH

Using simple algebra, you will find your answer for WH, women in the House.

Then just use Equation 4 again to find the number of men in the house.
Finally, add the men and women in the house to get the total number of
representatives.

Hope this is clear. Happy to be of help,

Josh

In article <3457b023.165736920@news.wenet.net>, Zero7404@aol.com (liz) wrote:

> I am working on this problem:
> There are 100 members in the Senate. The ratio of men to women in the
> Senate is 19:1
> The ratio of men to women in the House is 4:1
> The Senate and the House together have a ratio of men to women of 5:1
> How many members are in the House??
>
> I understand ratio when the total number is given (Senate), but when I
> get into the an unknown number I'm lost.
>
> I have worked out 19MS(men in senate) = WS(woman in senate) etc.
> MS + MH = 19WS + 4WH
>
> Hope someone can help. Thanks
>
>
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submissions: post to k12.ed.math or e-mail to k12math@sd28.bc.ca