Intuition

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Intuition

Postby 101dalmatians » Tue Apr 23, 2013 6:05 pm

Scaling??? How do you think through it??? (nsguy. please don't ans - I KNOW what ur gonna say)
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Re: Intuition

Postby rcoker7 » Tue Apr 23, 2013 6:47 pm

The way I'd recommend thinking about these is finding out a quantity that stays constant. For example, density is a common one.

Sometimes, however, nothing is held constant, and you have to think differently. Take this problem for example.

13C-46: A recipe for a dozen 2-in mild jalapeno cornbread muffins calls for 2 jalapenos. How many jalapenos are needed to make a gross(144) of 3-in spicy jalapeno cornbread muffins if spicy dough has 3 times as many jalapenos as mild dough?

My thought process for this problem is as follows. First, nothing obvious is held constant, so we have to do something differently. However, the last sentence says that spicy dough has 3 times as many jalapenos as mild dough. For now, I ignore this, since I can multiply by 3 at the end.

Now that we're ignoring that, we need to find what is held constant. It seems like the number of jalapenos should be proportional to the total volume of muffins, so our constant is (number of muffins)*(volume of muffins)/(number of jalapenos). Volume is proportional to (length)^3, so we have (12)(2)^3/(2)=(144)(3)^3/(x). After solving, we get x=81. Multiplying by 3, we get 243.

This is the general way I'd think through most scaling problems. Most of them are easier than this, so once you get the hang of "figuring out the constant" these should become much easier.
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