On a snowy winter's eve, two candles are lit at the exact same time. A 18-inch candle and a 21-inch candle are lit at the exact same time. The 18-inch candle burns 2 inches every hour. The 21-inch
candle burns 3 inches every hour.

b. x + 1

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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