Let’s complete the grid step-by-step:
First, consider the initial grid:
[tex]\[
\begin{array}{c|c|c|c}
\hline
x & & 20 & 3 \\
\hline
& 2000 & & 60 \\
\hline
6 & & 120 & 18 \\
\hline
\end{array}
\][/tex]
1. Find the missing value in the first row, second column:
- We know that:
[tex]\[
\text{Value at [0][1]} \times 6 = 2000
\][/tex]
- Solving for the missing value:
[tex]\[
\text{Value at [0][1]} = \frac{2000}{6} = 333
\][/tex]
- The updated grid looks like:
[tex]\[
\begin{array}{c|c|c|c}
\hline
x & 333 & 20 & 3 \\
\hline
& 2000 & & 60 \\
\hline
6 & & 120 & 18 \\
\hline
\end{array}
\][/tex]
2. Find the missing value in the second row, third column:
- We know that value:
[tex]\[
\text{Value at [1][2]} \times 20 = 2000
\][/tex]
- Solving for the missing value:
[tex]\[
\text{Value at [1][2]} = \frac{2000}{20} = 100
\][/tex]
- The updated grid looks like:
[tex]\[
\begin{array}{c|c|c|c}
\hline
x & 333 & 20 & 3 \\
\hline
& 2000 & 100 & 60 \\
\hline
6 & & 120 & 18 \\
\hline
\end{array}
\][/tex]
3. Find the missing value in the third row, second column:
- We know that value:
[tex]\[
6 \times \text{Value at [2][1]} = 18
\][/tex]
- Solving for the missing value:
[tex]\[
\text{Value at [2][1]} = \frac{18}{6} = 3
\][/tex]
- The updated grid looks like:
[tex]\[
\begin{array}{c|c|c|c}
\hline
x & 333 & 20 & 3 \\
\hline
& 2000 & 100 & 60 \\
\hline
6 & 3 & 120 & 18 \\
\hline
\end{array}
\][/tex]
Finally, as stated, the completed grid is:
[tex]\[
\begin{array}{c|c|c|c}
\hline
x & 333 & 20 & 3 \\
\hline
& 2000 & 100 & 60 \\
\hline
6 & 3 & 120 & 18 \\
\hline
\end{array}
\][/tex]
The answer is the resulting complete grid:
[tex]\[
\begin{array}{c|c|c|c}
\hline
\text{None} & 333 & 20 & 3 \\
\hline
\text{None} & 2000 & 100 & 60 \\
\hline
6 & 3 & 120 & 18 \\
\hline
\end{array}
\][/tex]
