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The number of kilograms of water in a human body varies directly as the mass of the body. A 93 kg person contains 62 kg of water. How many kilograms of water are in a 78 kg person?

Answer :

Answer:

52 kg

Steps:

Set both fractions equal to each other;

62/93 = x/78

62 * 78 = 93x

4836 = 93x

x = 52

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Rewritten by : Barada

A 78 kg person contains about 55.29 kg of water, following the direct variation from a 93 kg person with 62 kg of water.

In this scenario, we can use the concept of direct variation to find the amount of water in a 78 kg person.

Direct variation means that one quantity is directly proportional to another. In this case, the number of kilograms of water is directly proportional to the mass of the body.

First, we can establish a proportion using the information given:

[tex]\frac{(93 kg person's water) }{ (93 kg person's mass) }[/tex]= [tex]\frac{(78 kg person's water)}{ (78 kg person's mass)}[/tex]

Now, we can plug in the values:

[tex]\frac{62}{93}[/tex]= [tex]\frac{x}{78}[/tex]

To solve for x, we can cross-multiply:

62 [tex]\times[/tex]78 = 93 x

Now, solve for x:

x = [tex]\frac{62\times78}{93}[/tex]

x = [tex]\frac{5148}{93}[/tex]

x ≈ 55.29 kg

So, a 78 kg person contains approximately 55.29 kg of water.

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