Answer :
To answer this question, let's first understand the relationship given by the equation \( y = \frac{1}{6}x \), where \( y \) is the weight on the moon and \( x \) is the weight on Earth.
We need to complete the table with some ordered pairs \((x, y)\) and then find how much an object that weighs 36 kg on the moon would weigh on Earth.
### Step-by-Step Solution:
1. Identify Given Relationship:
The relationship between the weight on Earth \( x \) and the weight on the moon \( y \) is:
[tex]\[ y = \frac{1}{6}x \][/tex]
2. Create a Table of Ordered Pairs:
Let's calculate a few ordered pairs for different values of \( x \):
- If \( x = 6 \):
[tex]\[ y = \frac{1}{6} \times 6 = 1 \][/tex]
Ordered Pair: \((6, 1)\)
- If \( x = 12 \):
[tex]\[ y = \frac{1}{6} \times 12 = 2 \][/tex]
Ordered Pair: \((12, 2)\)
- If \( x = 18 \):
[tex]\[ y = \frac{1}{6} \times 18 = 3 \][/tex]
Ordered Pair: \((18, 3)\)
- If \( x = 24 \):
[tex]\[ y = \frac{1}{6} \times 24 = 4 \][/tex]
Ordered Pair: \((24, 4)\)
- If \( x = 30 \):
[tex]\[ y = \frac{1}{6} \times 30 = 5 \][/tex]
Ordered Pair: \((30, 5)\)
- If \( x = 36 \):
[tex]\[ y = \frac{1}{6} \times 36 = 6 \][/tex]
Ordered Pair: \((36, 6)\)
Now we can fill the table as follows:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline x & 6 & 12 & 18 \\ \hline y & 1 & 2 & 3 \\ \hline x & 24 & 30 & 36 \\ \hline y & 4 & 5 & 6 \\ \hline \end{tabular} \][/tex]
3. Find the Weight on Earth for 36 kg on Moon:
We are given that the object weighs 36 kg on the moon (\( y = 36 \) kg). We need to find the weight on Earth (\( x \)).
Using the equation \( y = \frac{1}{6} x \):
[tex]\[ 36 = \frac{1}{6} x \][/tex]
To solve for \( x \), we multiply both sides of the equation by 6:
[tex]\[ x = 36 \times 6 \][/tex]
[tex]\[ x = 216 \][/tex]
Therefore, an object that weighs 36 kg on the moon weighs 216 kg on Earth.
We need to complete the table with some ordered pairs \((x, y)\) and then find how much an object that weighs 36 kg on the moon would weigh on Earth.
### Step-by-Step Solution:
1. Identify Given Relationship:
The relationship between the weight on Earth \( x \) and the weight on the moon \( y \) is:
[tex]\[ y = \frac{1}{6}x \][/tex]
2. Create a Table of Ordered Pairs:
Let's calculate a few ordered pairs for different values of \( x \):
- If \( x = 6 \):
[tex]\[ y = \frac{1}{6} \times 6 = 1 \][/tex]
Ordered Pair: \((6, 1)\)
- If \( x = 12 \):
[tex]\[ y = \frac{1}{6} \times 12 = 2 \][/tex]
Ordered Pair: \((12, 2)\)
- If \( x = 18 \):
[tex]\[ y = \frac{1}{6} \times 18 = 3 \][/tex]
Ordered Pair: \((18, 3)\)
- If \( x = 24 \):
[tex]\[ y = \frac{1}{6} \times 24 = 4 \][/tex]
Ordered Pair: \((24, 4)\)
- If \( x = 30 \):
[tex]\[ y = \frac{1}{6} \times 30 = 5 \][/tex]
Ordered Pair: \((30, 5)\)
- If \( x = 36 \):
[tex]\[ y = \frac{1}{6} \times 36 = 6 \][/tex]
Ordered Pair: \((36, 6)\)
Now we can fill the table as follows:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline x & 6 & 12 & 18 \\ \hline y & 1 & 2 & 3 \\ \hline x & 24 & 30 & 36 \\ \hline y & 4 & 5 & 6 \\ \hline \end{tabular} \][/tex]
3. Find the Weight on Earth for 36 kg on Moon:
We are given that the object weighs 36 kg on the moon (\( y = 36 \) kg). We need to find the weight on Earth (\( x \)).
Using the equation \( y = \frac{1}{6} x \):
[tex]\[ 36 = \frac{1}{6} x \][/tex]
To solve for \( x \), we multiply both sides of the equation by 6:
[tex]\[ x = 36 \times 6 \][/tex]
[tex]\[ x = 216 \][/tex]
Therefore, an object that weighs 36 kg on the moon weighs 216 kg on Earth.
