Joy organized a wedding. guests had to choose their meal from beef, chicken or vegetarian.1/3 of the guests chose beef5/12 of the guests chose chicken23 of the guests chose vegetarian how many guests were at the wedding? in detailed steps

Let the number of guests at the wedding be represented by "g"

The number of people who take beef = 1/3*g = g/3

The number of people who opt for chicken = 5/12*g = 5g/12

The number of people who opt for vegetarian = 23

So, g/3 + 5g/12 + 23 = g since "g" is the total guests

Now,we need to solve for g

g/3 + 5g/12 + 23 = g

g-g/3-5g/12 = 23

(12g-4g-5g)/12 = 23

3g = 276

g = 276/3

g = 92

Total number of guests at the wedding = 92

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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