On a shopping trip, peter spent 1/3 of his money for a jacket and $5 for a hat. if peter still had half of his money left, how much did he have originally?

Let x represent the money he originally had

x = x + 5

x - x = 5

x - x = 5

x = 5

x = 30

$30

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+

25.45584