Algebra Problem Watch

ΘTheta
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#1
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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!
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Smaug123
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(Original post by ΘTheta)
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!
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.
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TeeEm
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(Original post by ΘTheta)
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!
I also got 196 ...
I must be doing the same mistake like you despite my equations being different.
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Smaug123
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(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.
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ΘTheta
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(Original post by Smaug123)
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.
Hello there. Thanks for the advice, but drawing the triangles aren't really helping, sorry.

How would you solve it using equations? Thanks!
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TeeEm
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(Original post by Smaug123)
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.
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!
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Smaug123
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(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
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ΘTheta
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#8
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(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!
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Smaug123
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(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!
28, because the lead R has over B reduces by 56, which means B gains 28 and R loses 28.
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ΘTheta
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(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!
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TeeEm
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#11
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(Original post by ΘTheta)
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!
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.
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