the number of kilograms of water in a human body varies directly as the mass of the body an 87kg person contains 58kg of water how many kilograms of water are in a 72-kg person
water = k(bodymass) where k is a constant
for the given case
58 = k(87)
k= 58/87
= 2/3
water = (2/3)(bodymass)
so if bodymass = 72
water = (2/3)(72) = 48
To determine the number of kilograms of water in a 72-kg person, we can use the concept of direct variation.
Let's set up a proportion using the given information:
Mass of person 1 / Mass of water in person 1 = Mass of person 2 / Mass of water in person 2
Plugging in the values we know:
87 kg / 58 kg = 72 kg / x
To find x, we can solve the proportion:
87 kg * x = 58 kg * 72 kg
87x = 4176 kg²
To isolate x, we divide both sides of the equation by 87:
x = 4176 kg² / 87
x ≈ 48 kg
Therefore, a 72-kg person contains approximately 48 kg of water.
To solve this problem, we need to understand the concept of direct variation. In direct variation, two quantities are directly proportional to each other. This means that when one quantity changes, the other changes in the same ratio.
Let's say the mass of the body is denoted by "m" and the amount of water in kilograms is denoted by "w". According to the problem, the number of kilograms of water (w) varies directly with the mass of the body (m).
We can set up a proportion to solve for the unknown quantity of water, given the mass of the body:
w₁ / m₁ = w₂ / m₂
where w₁ and m₁ represent the known values, and w₂ is the unknown value we want to find.
Given:
m₁ = 87 kg (mass of the first person)
w₁ = 58 kg (amount of water for the first person)
m₂ = 72 kg (mass of the second person)
w₂ (unknown)
Plugging these values into the proportion, we have:
58 kg / 87 kg = w₂ / 72 kg
To find w₂, we can cross-multiply and solve for it:
w₂ = (58 kg / 87 kg) * 72 kg
w₂ = 48 kg
Therefore, a 72-kg person would contain approximately 48 kg of water.