Quote (Kokua @ May 2 2017 01:24am)

they already bought the cake though.
the silly thing is that they gave frank what would likely be his least favorite piece as opposed to what the other 8 pieces could possibly be.
the other silly thing is that whoever made the cake make is so out of it that the cake ended up having different amounts of chocolate and chocolate with each slice.
a possible reason for this could be that it was a chocolate filled center cake, and he ended up getting a corner piece that was mostly sponge.
the questions asks how much would frank value that specific slice, not that he is paying specifically for that slice.

i was thinking it over last night, and if you cut a cake into 9 slices and look at each slice in terms of 4 quarters, that makes the value of 1/36 of sponge worth $0.50 and 1/36 of chocolate worth $1.00 in terms of frank's own personal preference, with 12/36 of the cake being sponge and 24/36 of the cake being chocolate.
this does not mean that frank pays this specific amount for this specific slice. the entire cake was purchased regardless of what each individual values different parts of the cake as.
the question is, how much does frank value the slice that he received. his slice was 3/36 sponge and 1/36 chocolate, in regards of portion to the whole cake, giving it 3*$0.50 + 1+$1.00 = $2.50.
if there was anything in this question that asked for an argument, the argument should be that frank should receive a slice that is 3/4 chocolate and 1/4 sponge as opposed to the slice he received (assuming such a slice exists), as he would then value that slice at $3.50, a whole dollar more than the slice he was given.

if you read the question closely, it doesn't say anything close to them buying a specific slice.
they bought a cake for $30.
they then cut that cake into 9 pieces.
he likes chocolate twice as much as sponge.
thus we assume he values chocolate twice as much as sponge.
he was given a slice that was 3/4 sponge, and 1/4 chocolate.
we are only asked to figure how much frank would personally value this specific slice. keep in mind the first line, they already bought the whole cake.