A measure of malnutrition, called the pelidisi, varies directly as the cube root

Question

A measure of malnutrition, called the pelidisi, varies directly as the cube root of a person's weight in grams and inversely as the person's sitting height in centimeters. A person with a pelidisi below 100 is considered to be undernourished, while a pelidisi greater than 100 indicates overfeeding. A person who weighs 48,820 g with a sitting height of 78.7 cm has a pelidisi of 100. Find the pelidisi (to the nearest whole number) of a person whose weight is 56 comma 57156,571 g and whose sitting height is 63.263.2 cm. Is this individual undernourished or overfed?

Explanation / Answer

since , P varies directly as the cube root of a person's weight in grams and inversely as the person's sitting height in centimeters

P = k cube root ( W ) / H

where , P = pelidisi

W = weight

H = height

k = proportionality constant

A person who weighs 48,820 g with a sitting height of 78.7 cm has a pelidisi of 100

we can write , 100 = k cube root ( 48820 ) / 78.7

100 = k (36.548 ) / 78.7

k = 100 * 78.7 / 36.548 = 215.33

now finding pelidisi for weight = 57156,571 g and height = 63.2632

P = 215.33 cube root ( 57156.571 ) / 63.2632 = 131.11

pelidisi greater than 100 indicates overfeeding

thus individual is overfed

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