Posted by Melissa on Wednesday, September 10, 2008 at 9:05am.
No, Bob didn't set it up that way. He simply used dimensional analysis to work the problem AND he noted to you to see that the units you don't want cancel and leaves the units you want; i.e., cars.
64 inches x (6 cars/16 inches) = 24 cars.
If you prefer, it can also be done as a proportion.
(6 cars/16 inches) = (x cars/64 inches)
Now cross multiply to get
16x=6*64
x = 6*64/16 = 24 cars
Can I throw in a note of clarification? Melissa'a answers are actually correct: what's INcorrect is the algebra that apparently gave rise to them. As Bob pointed out, the "16 divided by 6" is actually a measure of inches per car, not cars per inch. Also, the three next statements give the right answers (24, 15 and 39 cars respectively), but 64 x 2.66 is not 24, 40 x 2.66 is not 15, and 104 x 2.66 is not 39, so if you were being marked on your working, you'd have lost marks there. These equations OUGHT to read 64 / 2.66 = 24, 40 / 2.66 = 15 and 104 / 2.66 = 39.
Bob's point is that you can verify that you haven't made a silly mistake like dividing by a factor when you should have been multiplying by it by checking the dimensional consistency of the equation - and that's a good habit to get into, as mistakes like this are very easy to make. For example, if you wrote the first equation in full, you would get
64 in x 2.66 in/car = <whatever it is> inē/car
and you would be able to see immediately that that was wrong, since what you OUGHT to get is a number of cars (as opposed to a number of square inches per car, whatever that means). If you had divided the 2.66 factor into the 64 inches instead, you would have got it right, because you would get
64 in / (2.66 in/car) = <whatever it is> cars.
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