Algebra Problem

Hi guys, I need help with this question.

In a particular country there are two political parties, the Red Party and the Blue Party. Prior tolast week's General Election the Red Party had 2½ times as many representatives in theparliament as the Blue Party. The Red Party's lead has been reduced by 56 as a result of theGeneral Election, but it now has 1½ times as many representatives as the Blue Party.
How many seats are there in the parliament?

So since the Red party has 2.5times as many people as the blue party, I did 2.5x+1x=T (for total people in the government).
Then after wards, I did 1.5x+1x+56=T
After solving for I got the total as 196, which I wrong. So I'm wondering where I wen't wrong?
Thanks!

Reply 1

Smaug123

Original post by ΘTheta

The *lead* has been reduced. That is, R-B has been reduced, not T. (I'd personally work with R and B throughout, rather than x; that makes it easier for me to remember which variable is talking about what.)

It may help to draw a picture. A rectangle with a proportion 5:2 in favour of Red, then a rectangle below it with the swing decreased by 56, and in 3:2 ratio.

Reply 2

TeeEm

Original post by ΘTheta

I also got 196 ...
I must be doing the same mistake like you despite my equations being different.

Reply 3

Smaug123

Original post by TeeEm

I also got 196 ...
I must be doing the same mistake like you despite my equations being different.

It's not 196. That would mean:
R before = 140, B before = 56
Then lead reduced by 56, so the new lead is 28; that gives R = 112, B = 84.
But 112/196 is 4/7 (in particular, not 3/5).

If you work through that with x instead of 196, you should get the answer popping out at the end.

(edited 9 years ago)

Reply 4

ΘTheta

Original post by Smaug123

Hello there. Thanks for the advice, but drawing the triangles aren't really helping, sorry.

How would you solve it using equations? Thanks!

Reply 5

TeeEm

Original post by Smaug123

you are probably right cause I am multitasking at present so I did not read the question carefully

the lead was cut and and not the number of reds

rep for being awake at this time!

(edited 9 years ago)

Reply 6

Smaug123

Original post by ΘTheta

Hello there. Thanks for the advice, but drawing the triangles aren't really helping, sorry.

How would you solve it using equations? Thanks!

The only way I formulated the correct equations was by drawing diagrams :P

2014-10-30 23.03.25.jpg504.3KB

Reply 7

ΘTheta

Original post by Smaug123

The only way I formulated the correct equations was by drawing diagrams :P

Oh. I done something similar, but I ended up getting 490 (which is half of the answer of 245). I think it was because I used a gap of 56, where as you used 28. Why did you use 28? Thanks! :biggrin:

Reply 8

Smaug123

Original post by ΘTheta

Oh. I done something similar, but I ended up getting 490 (which is half of the answer of 245). I think it was because I used a gap of 56, where as you used 28. Why did you use 28? Thanks! :biggrin:

28, because the lead R has over B reduces by 56, which means B gains 28 and R loses 28.

Reply 9

ΘTheta

Original post by Smaug123

28, because the lead R has over B reduces by 56, which means B gains 28 and R loses 28.

I see. Thanks! :smile:

Reply 10

TeeEm

Original post by ΘTheta

look at the attached question. Not the same as yours but almost ...

Enlarge the PDF solution attached.

CANON Lide.pdf

see if this modelling makes things clearer.