To find the constant of proportionality for the ratio of the price to the number of bouquets from the given table, you need to follow a series of steps involving division and observation. Here's a detailed, step-by-step solution:
1. Extract Information from Table:
The table provides the following data:
- Number of Bouquets: 3, 6, 9, 12
- Prices: [tex]$9, $[/tex]18, [tex]$27, $[/tex]36
2. Calculate the Ratios:
For each row in the table, compute the ratio of price to the number of bouquets. This ratio should be consistent if the variables are proportional.
3. Compute the Ratio for Each Data Point:
- For 3 bouquets costing [tex]$9:
\[
\text{Ratio} = \frac{\text{Price}}{\text{Number of Bouquets}} = \frac{9}{3} = 3
\]
- For 6 bouquets costing $[/tex]18:
[tex]\[
\text{Ratio} = \frac{18}{6} = 3
\][/tex]
- For 9 bouquets costing [tex]$27:
\[
\text{Ratio} = \frac{27}{9} = 3
\]
- For 12 bouquets costing $[/tex]36:
[tex]\[
\text{Ratio} = \frac{36}{12} = 3
\][/tex]
4. Observe the Ratios:
All computed ratios (3, 3, 3, 3) are consistent and equal. This consistent ratio is the constant of proportionality.
5. Conclude the Constant of Proportionality:
Since the ratio of price to the number of bouquets is consistently 3, we determine that the constant of proportionality is:
[tex]\[
k = 3
\][/tex]
Therefore, the constant of proportionality for the ratio of the price to the number of bouquets is 3. This means that for each bouquet, the price increases by $3.
