The ratio of the number of Mary's necklaces to the number of Helen's necklaces is 25:9.Mary's has 100 necklaces. How many necklaces does Helen's have.

36

Step-by-step explanation:

Given

The ratio of Mary's to Helen's necklaces is 25:9

Mary has 100 necklaces

Suppose Helen has x necklaces

Therefore the ratio can be written like

So, Helen has 36 necklaces

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