Ingrid and frank buy a cake for $30 that is one third sponge and two-thirds chocolate and cut the cake into 9 slices. If frank likes chocolate twice as much as sponge, what is the value of slice to him that is one-quarter chocolate and three-quarters sponge?

Really a vague question -

I came up with the slice is worth $3.33 regardless making each 1/4 worth .8325 cents.

Assuming he is willing to pay double for the 1/4 chocolate then i have 1.665+.8325+.8325+.8325 = $4.1625 for the slice. =/= 4.17 (Business is greedy)

If it were a "fair share" the piece is only worth 3.33 regardless of the flavor.

Super vague, plus... who makes a cake that is so disproportionate that you have a 2/3 chocolate and 1/3 sponge, but you get a slice with 1/4 chocolate! Thats bad cake making.

I agree with your numbers tho overall.

3 *price (sponge) + 6 *price (chocolate)= 30
2*price (sponge) = price (chocolate ).

Solve for price of sponge and chocolate.

Price(chocolate) = 4
Price (sponge) = 2

1/4 * price (chocolate) + 3/4 * price (sponge) = (1/4)*4 + (3/4)*2 = 2.5





Not sure why you guys are giving advice when you clearly don't understand the question...

This post was edited by sentries on Apr 30 2017 11:19am

The question doesn't state that only Frank is buying cake, if that were the case the sales of the cake would change.
Why is Ingrid paying more than a fair share for a cake slice that does not have preference of? I don't agree with your response.

30/9=3.33
each slice = 3.33
Ingrid has no preference = 3.33 per slice.
Frank is willing to pay double for a portion of the same size slice, your answer = 2.50

This post was edited by Astroglide420 on May 1 2017 07:49am

$30 cake
likes chocolate twice as much as sponge
thus, values chocolate twice as much as sponge
1/3 sponge = 1/2 the value of 1/3 chocolate
1/3 sponge = $6 while 1/3 chocolate = $12 with a total of 2/3 chocolate in the cake
$6 + ($12 * 2) = $30 cake
9 slices
1 slice with 1/4 chocolate and 3/4 sponge
(1/(4*9)) * $24) + (3/(4*9)) * $6) = $1.16.66 repeating, or $1.17 rounded.

they paid $30 for the cake, they are not discussing how much each of them will pay for the cake, but rather their personal value of the slice that they received.
the value of this particular slice is rather low, due to a high amount of a low valued ingredient (sponge) in the slice, and a low amount of a high valued ingredient (chocolate).

This post was edited by Kokua on May 1 2017 09:48am

How will the rest of the cake value at this price? at the given price we lost money on the cake.

This post was edited by Astroglide420 on May 1 2017 09:50am

assuming whoever made the cake turned it into a tornado and made wildly uneven portions in the cake, you may even end up with a slice that is 100% chocolate, and the value of that particular slice will be much higher than the value of a slice that is 3/4 sponge when the entire cake is 1/3 sponge.
i do see what you mean though, and im looking over a few things.

3(1/(4*9)) * $24) + 1.5(3/(4*9)) * $6) = $2.5
multiplying the sponge by 3 and the chocolate by 1.5, from my original calculations brings the value of the sponge and chocolate at their appropriate prices >_>
multiplying by 3 to sponge would bring a full 12/36 amount of sponge to $6 like i previously mentioned, and 1.5 to chocolate would bring the full 24/36 amount it up to $24. i missed that somewhere along the way
now i'm curious where i originally went wrong, and how that can be changed.

ah i see, i used the total value of chocolate and sponge in the cake rather than their individual and equal amount values.


This post was edited by Kokua on May 1 2017 10:07am

I understand your math
I would still make the argument that the cake isn't going to sell because frank is only buying one slice and not everybody is going to pay double for the chocolate.

really a silly worded question.

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.