Adam made note of all the bicycles and cars he could see parked or locked on a certain city block. All the cars had exactly four wheels, and all the bicycles had exactly
two wheels. How many wheels were on the block if there were 15 bicycles and 7 cars?
How many wheels were on the block if there were x bicycles and y cars?

Answer  

68 bicycles.  

Let there be x bicycles, then there are (93 - x) tricycles.

From the given values:

2x + 3(93 - x) = 211

2x + 279 - 3x = 211

-x = 211 - 279 = -68

x = -68/-1 = 68.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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