Answer :
Certainly! Let's work through the solution step-by-step:
1. Understanding the Problem:
- We know that the number of kilograms of water in a human body varies directly with the body's mass. This means if the body mass increases, the water content also increases at a constant rate.
2. Given Information:
- For a person weighing 90 kg, there are 60 kg of water in their body.
3. Direct Variation Formula:
- The relationship between the body mass (m) and water mass (w) is given by: [tex]\( w = k \times m \)[/tex]
- Here, [tex]\( k \)[/tex] is the constant of proportionality.
4. Finding the Constant of Proportionality ([tex]\( k \)[/tex]):
- Using the given values (for a 90 kg person with 60 kg of water):
[tex]\[
60 = k \times 90
\][/tex]
- Solving for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{60}{90} = \frac{2}{3} \approx 0.67
\][/tex]
5. Finding the Amount of Water in a 159 kg Person:
- Now that we know [tex]\( k \approx 0.67 \)[/tex], we can find out how much water is in a 159 kg person:
[tex]\[
w = k \times 159
\][/tex]
[tex]\[
w = 0.67 \times 159 \approx 106 \text{ kg}
\][/tex]
6. Conclusion:
- A 159 kg person contains approximately 106 kg of water.
So, a 159 kg person has approximately 106 kilograms of water in their body.
1. Understanding the Problem:
- We know that the number of kilograms of water in a human body varies directly with the body's mass. This means if the body mass increases, the water content also increases at a constant rate.
2. Given Information:
- For a person weighing 90 kg, there are 60 kg of water in their body.
3. Direct Variation Formula:
- The relationship between the body mass (m) and water mass (w) is given by: [tex]\( w = k \times m \)[/tex]
- Here, [tex]\( k \)[/tex] is the constant of proportionality.
4. Finding the Constant of Proportionality ([tex]\( k \)[/tex]):
- Using the given values (for a 90 kg person with 60 kg of water):
[tex]\[
60 = k \times 90
\][/tex]
- Solving for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{60}{90} = \frac{2}{3} \approx 0.67
\][/tex]
5. Finding the Amount of Water in a 159 kg Person:
- Now that we know [tex]\( k \approx 0.67 \)[/tex], we can find out how much water is in a 159 kg person:
[tex]\[
w = k \times 159
\][/tex]
[tex]\[
w = 0.67 \times 159 \approx 106 \text{ kg}
\][/tex]
6. Conclusion:
- A 159 kg person contains approximately 106 kg of water.
So, a 159 kg person has approximately 106 kilograms of water in their body.
