Answer :
Sure! Let's work through the problem step by step.
The problem states that the number of kilograms of water in a person's body varies directly as the person's mass. This means if you know the person's mass, you can calculate the amount of water using a direct variation relationship.
### Direct Variation Formula
When two quantities vary directly, you can use the formula:
[tex]\[ \text{water\_mass} = k \times \text{person\_mass} \][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
### Given
- A person with a mass of 90 kg contains 60 kg of water.
- We need to find out how many kilograms of water are in a person whose mass is 75 kg.
### Step 1: Determine the Constant of Variation ([tex]\( k \)[/tex])
From the given information:
- [tex]\( \text{water\_mass} = 60 \)[/tex] kg when [tex]\( \text{person\_mass} = 90 \)[/tex] kg.
Using the direct variation formula:
[tex]\[ 60 = k \times 90 \][/tex]
To find [tex]\( k \)[/tex], divide both sides by 90:
[tex]\[ k = \frac{60}{90} \][/tex]
[tex]\[ k = \frac{2}{3} \][/tex]
### Step 2: Calculate Water Mass for a 75 kg Person
Now that we have the constant [tex]\( k = \frac{2}{3} \)[/tex], we can find the water mass for a person with a mass of 75 kg.
Using the formula again:
[tex]\[ \text{water\_mass} = k \times 75 \][/tex]
[tex]\[ \text{water\_mass} = \frac{2}{3} \times 75 \][/tex]
Calculate the result:
[tex]\[ \text{water\_mass} = 50 \][/tex]
### Final Answer
Therefore, a person with a mass of 75 kg contains 50 kg of water. The correct answer is F. 50kg.
The problem states that the number of kilograms of water in a person's body varies directly as the person's mass. This means if you know the person's mass, you can calculate the amount of water using a direct variation relationship.
### Direct Variation Formula
When two quantities vary directly, you can use the formula:
[tex]\[ \text{water\_mass} = k \times \text{person\_mass} \][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
### Given
- A person with a mass of 90 kg contains 60 kg of water.
- We need to find out how many kilograms of water are in a person whose mass is 75 kg.
### Step 1: Determine the Constant of Variation ([tex]\( k \)[/tex])
From the given information:
- [tex]\( \text{water\_mass} = 60 \)[/tex] kg when [tex]\( \text{person\_mass} = 90 \)[/tex] kg.
Using the direct variation formula:
[tex]\[ 60 = k \times 90 \][/tex]
To find [tex]\( k \)[/tex], divide both sides by 90:
[tex]\[ k = \frac{60}{90} \][/tex]
[tex]\[ k = \frac{2}{3} \][/tex]
### Step 2: Calculate Water Mass for a 75 kg Person
Now that we have the constant [tex]\( k = \frac{2}{3} \)[/tex], we can find the water mass for a person with a mass of 75 kg.
Using the formula again:
[tex]\[ \text{water\_mass} = k \times 75 \][/tex]
[tex]\[ \text{water\_mass} = \frac{2}{3} \times 75 \][/tex]
Calculate the result:
[tex]\[ \text{water\_mass} = 50 \][/tex]
### Final Answer
Therefore, a person with a mass of 75 kg contains 50 kg of water. The correct answer is F. 50kg.
