a clothing manufacturer has 1,000 yd of cotton to make shirts and pajamas. a shirt requires 1 yd of fabric, and a pair of pajamas requires 2 yd of fabric. It takes 2 hours to make a shirt and 3 hours to make the pajamas, and there are 1,600 hours available to make the clothing

step-by-step explanation:

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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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