Kelly spends $63.90 on items for a party. she buys you cards that cost $5.40 (including tax). she also buys gift bags that cost $11.70 each. if she buys one gift bag for each guest, how many guests did kelly invite to the party?
a.
6
b.
5
c.
8
d.
4

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