Shrimp Problem

[ENHSmath]

Fried Shrimp is coated with a constant thickness of batter before frying. Shrimp count is the number of shrimp in a pound. If it takes 3 cups of flour to make enough batter for 3 dozen 24-count shrimp, how much flour is needed for batter for 5 dozen 12-count shrimp?

[Shawn]

This solution was improperly calculated see post below
It is a scaling problem with surface area and volume answer would help to know if I am right. I will just quickly give my best guess though:

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Let me know if this is right or wrong, so I can either post an explanation or fix my solution

[101dalmatians]

Cool! Thanks for the scaling! I had a few qs about that too but they are all cleared... :)

[Shawn]

Is the answer correct?

[101dalmatians]

idk

[ENHSmath]

[Shawn]

That makes sense.
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[unparseable or potentially dangerous latex formula]

The scaling is volume and surface area. The volume is slightly more difficult to think about. If you have 12 shrimp vs 24 shrimp to a pound, this means more the the shrimp will be exposed to the air (think of 1 large ball vs 1000 small balls same total mass). But since the unit is shrip/pound you need to inverse he unit to be a volume unit pound/shrimp, which with a constant density is volume. After you inverse the unit it is fairly simple. You then just have to get all given units to be suface area. Volume to a linear unit is done by taking the cubic root (x^1/3) and after you have linear you need to square (x^2) it to get to surface area. So if you combine these you get x^(2/3). The quanties are already proportional so just tack on a multiplier. This gets you the scaling set up above. If you have any other questions, feel free to post them. I am trying to once again follow this forum.

-Shawn

[101dalmatians]

coOl :O

[ENHSmath]

Thank you Shawn.