There is a new country called saffron where the peoples...

There is a new country called Saffron where the people's political opinions lead them to divide themselves into five different groups, representing different outlooks on how the legislature should approach public policy. These five groups based on political convictions in turn result in the formation of five political parties (each named after a type of food). The five parties are listed below in order from most liberal to most conservative. In the first election for the legislature in this country the people vote for their candidates and their parties as follows, with the vote in the whole country being the same as the vote in every part of it:

Transcript

00:01 So in this problem, we're working with a political science class at a large university.

00:21 And we asked the students first to determine if they are liberal or conservative.

00:35 And we asked the same question at the end of the course, trying to see what effect our discussions had on it.

00:40 And what we find out is that those that characterize themselves as liberal initially, well, 30 % went to conservative and those that were initially conservative 40 % went over to liberal and it turns out that we had just as many students with conservative views at the end as there had been liberal students at the beginning so conservative at end was the same as liberal at let me let me i'm putting all the liberal stuff on the left hand side so let me fix this up so it's consistent here so we have conservative at the end is the same as liberal at the beginning and we have 260 total students nobody adds nobody drops so we have the same number of students that we started with at we end up with the end so what we're asked then is how many liberal and how many conservative students did we begin with and end that's the real question here okay so let's do this let x be the number of conservative students at the beginning.

03:42 Okay, well, if 40 % of them went over to liberal, then what does that mean? that means 0 .6x is the number of conservative students at the end.

04:11 Okay? and there were 260 minus x will be the number of liberal students at the beginning, because they're either liberal or conservative, one of the two.

04:38 Okay? and it says that 30 % went to conservative.

04:48 So at the end, i only have 30 % less, which means i have 0 .7 times 260 minus x is the number of liberal students at the end.

05:16 And so at the end, the total number of conservative students at the end, well, that's the 0 .6x that i started with, plus, right, this 30 % of the liberal students that came over, 260 minus x, and that's equal to 260 minus x, isn't it? because we said that the liberal at the beginning, liberal at the beginning, which is this piece here, is the same as the conservatives at the end.

07:00 Well, the conservatives at the end is all of this, isn't it? okay, so distribute the point three.

07:11 So this is 0 .6x plus 78 minus 0 .3x is equal...

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