Question

the composition of an animal is defined as the muscles, bones, and fat of the animal. a scientist studied the composition of one young swamp buffalo and determined the buffalo had 134.6 kilograms of muscle, which made up approximately 65.4% of its composition. of the remaining composition of this buffalo, approximately 47.9% was bone, and the remainder was fat. based on these approximations, to the nearest tenth, how many kilograms of this buffalos composition was fat?

Explanation:

Step1: Find the total composition of the buffalo

Let the total composition of the buffalo be \(x\) kilograms. We know that the muscle is \(134.6\) kilograms and it makes up \(65.4\%\) of the composition. So we can set up the equation \(\frac{134.6}{x}=0.654\). Solving for \(x\), we get \(x = \frac{134.6}{0.654}\approx205.8\) kilograms.

Step2: Find the percentage of fat

The percentage of bone is \(47.9\%\) of the non - muscle composition. The non - muscle composition is \(100 - 65.4=34.6\%\) of the total. So the percentage of fat in the total composition is \((1 - 0.654)\times(1 - 0.479)=0.346\times0.521 = 0.180266\)

Step3: Calculate the kilograms of fat

Multiply the total composition \(x\approx205.8\) by the percentage of fat \(0.180266\). So the kilograms of fat is \(205.8\times0.180266\approx37.1\)

Answer:

\(37.1\)