Three friends, Angie, Beth, and Carl are trying to split a cake worth 36 dollars. One half of the cake is vanilla, the other half is chocolate. Angie likes vanilla and chocolate the same, Beth likes vanilla three times more than she likes chocolate, and Carl likes chocolate twice as much as he likes vanilla. (3 points) (a) How much does each person value each half of the cake? (7 points) (b) Angie gets to cut first and she cuts the cake into two pieces. One of the pieces is 2/3 vanilla and 1/3 chocolate. The other piece is 1/3 vanilla and 2/3 chocolate. Beth now gets to choose one of the pieces. Which one will she choose? Justify this by showing what each piece is worth to her. (10 points) (c) Now, Carl gets to choose his cake from Angie's and Beth's pieces. Indicate how Angie and Beth would divide their pieces and which pieces Carl would select. Specify how much Carl's pieces will be worth to him (You may leave your answer as a fraction).please tell me how to calculate the answer and the reason why they should calculate that way.