 In this video, we provide the solution to question number 14 for practice exam number two for math 1030, in which case we have Brad and Angelina jointly, they buy together a half strawberry, half chocolate cake that is worth $36 total. Now, suppose that Angelina values the chocolate cake side twice as much as she values the strawberry cake side. So I actually wanna look at that for a moment. If she values the chocolate side C at twice the value of the strawberry side, so two S there, the collectively these things are worth $36 there. So if we substitute this in like so, we can replace the C with a two S there. We get two S plus S is equal to 36. You end up with three S is equal to 36. If you divide both sides by three, then S here is worth 12. So Angelina values the strawberry side of the cake at $12 and thus she values the chocolate cake at $24. Notice that 24 plus 12 gives you 36. So that's how she values the two chunks of the cake there. Okay, Brad is gonna be a lot easier in this situation. Brad values the two flavors exactly the same. So for his sake, so this is like the Angelina side. If you look at the Brad side, his is much easier. The chocolate he values at $18 and at the strawberry he values as $18 because he doesn't see a difference between the two flavors. No value there, no difference value. Okay, so they're gonna divide the cake using the divider chooser method. So I cut you choose. Brad is going to cut the cake. And so he's gonna cut the cake according to the illustration. He's gonna cut the cake along this diagonal line so that you get two thirds of the chocolate on the left slice and one third of the strawberry on the left slice. And then you get one third of the chocolate here and then two thirds of the strawberry here. That way, maybe trying to be a gentleman here, that way Angelina can pick the flavor that she likes the most, okay? So we're gonna call this cake slice on the left, share one and this cake slice on the right, share two. So how are they gonna value these things? Well, Brad is pretty easy. Brad is going to value share one as much as share two. They're gonna both be $18 to him. But that was, we didn't even need to know Brad's value system to do this because he's the divider and a divider chooser. Both of those two slices are gonna be of equal value, a fair share, which is $18, okay? But of course, to make this a legitimate cut, a rational cut, we did have to describe Brad's value system there. So coming back to then Angelina here, we wanna calculate how much she values the two shares. So share one is gonna have two thirds the value of the chocolate slice, see there, plus one third the value of the strawberry slice, for which the chocolate slice we've already figured out is worth $24 to her and the strawberry is worth 12. So simplifying those things, three goes into 24 eight times and three goes into 12 four times there. Two times four is equal to, sorry, two times eight is equal to 16 plus four. She values the first slice at $20 and then how about the second slice, S2 here? Well, it has one third the chocolate plus it has two thirds the strawberry, for which we can go through the details of this. Again, you get 24 over three plus two times 12 over three, for which as we saw before, three goes into 24 eight times, three goes into 12 four times. You get two times four, which is eight, eight plus eight is worth 16, but that's not too surprising, given that the total cake was $36. If we know share one is valued to 20, we could just done 36 minus 20 to get you 16. So these are how much they value the cakes. So Angelina says the share one is worth 20, that the share two is worth 16, Brad values both of them at $18. So it's pretty clear what we're gonna see here. Let's give an explicit answer here. Angelina gets, that doesn't quite fit there. Let's make this look longer. There we go. Angelina gets share one valued at $20 and then Brad gets share two valued at $18. And that then would be the distribution of assets amongst these two players in the game.