To determine the missing values in the table, we can identify the relationship between the number of tables and the number of chairs. Since it is given that the number of tables and chairs is proportional, we can write this relationship as:
\[ \text{Chairs} = k \times \text{Tables} \]
Where \( k \) is a constant.
From the data provided, we have the following pairs:
- \( 1 \) table \( \Rightarrow 6 \) chairs
- \( 2 \) tables \( \Rightarrow 18 \) chairs
- \( 4 \) tables \( \Rightarrow 24 \) chairs
- \( 5 \) tables \( \Rightarrow ? \) chairs
- \( ? \) tables \( \Rightarrow 36 \) chairs
Let's first calculate the constant \( k \) using any of the given pairs. Using the first pair:
When \( 1 \) table: \[ k = \frac{6 \text{ chairs}}{1 \text{ table}} = 6 \]
Now we can fill in the missing values:
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For \( 5 \) tables: \[ \text{Chairs} = 6 \times 5 = 30 \]
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Now, for the number of tables corresponding to \( 36 \) chairs: \[ 6 \text{ chairs} = k \times \text{Tables} \implies 36 = 6 \times \text{Tables} \] \[ \text{Tables} = \frac{36}{6} = 6 \]
Now filling in the table with the calculated values:
| Tables | Chairs | |--------|--------| | 1 | 6 | | 2 | 18 | | 4 | 24 | | 5 | 30 | | 6 | 36 |
So, the missing values are:
- \( 5 \) tables -> \( 30 \) chairs
- \( 6 \) tables -> \( 36 \) chairs
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