Bot GPT 4-o mini To determine if there is a proportional relationship between the number of dozens of eggs and the cost, we need to see if the ratio of cost to dozen is constant for all pairs in the table.
What you provided seems like a partial dataset. For simplicity, let's look at the pairs you've given. We'll examine the pairs of dozens and their associated costs; it looks like the numbers may be as follows:
- 4 dozens of eggs cost $6
- 8 dozens of eggs cost $10
- 12 dozens of eggs cost $15
- 16 dozens of eggs cost $24
Let's calculate the ratios (cost per dozen):
-
For 4 dozens costing $6:
\(\frac{6}{4} = 1.5\) (cost per dozen) -
For 8 dozens costing $10:
\(\frac{10}{8} = 1.25\) (cost per dozen) -
For 12 dozens costing $15:
\(\frac{15}{12} = 1.25\) (cost per dozen) -
For 16 dozens costing $24:
\(\frac{24}{16} = 1.5\) (cost per dozen)
The ratios are:
- 1.5 for 4 dozens
- 1.25 for 8 dozens
- 1.25 for 12 dozens
- 1.5 for 16 dozens
Since these ratios are not constant (they change for different amounts of dozens), the table does not show a proportional relationship between the number of dozens of eggs and the cost.
Now, regarding which ratio would be more useful to someone going to the wholesale club, let's evaluate both options:
- \(\frac{\text{cost}}{\text{dozen}}\) tells you how much you pay for each dozen of eggs. This is useful to understand the price you would pay per dozen.
- \(\frac{\text{dozen}}{\text{cost}}\) giving you the number of dozens you can buy for a certain amount of money, which is less commonly used.
The ratio \(\frac{\text{cost}}{\text{dozen}}\) (cost per dozen) would be more useful because customers generally want to know how much they need to pay for each dozen when shopping.
Summary:
- Part 1 answer: The table does not show a proportional relationship between the number of dozens of eggs and the cost.
- Useful ratio: \(\frac{\text{cost}}{\text{dozen}}\) – it informs buyers of the price per dozen.
3 answers