Final answer:
To determine whether a table shows a proportional relationship, the ratio between values should be consistent. For example, if 1 pudding cup costs $3, then 2 should cost $6, etc. Without seeing the actual table, option (a) suggests a proportional relationship if the price per cup is $3, while option (c) implies there is no proportional relationship if the price per cup is believed to be different, such as $2.
Step-by-step explanation:
To determine if the table of numbers represents a proportional relationship, we need to see if the ratio of the price to the number of pudding cups is consistent.
A relationship is proportional if the ratio is constant throughout the table. For instance, if 1 pudding cup costs $3, then 2 cups should cost $6, 3 cups should cost $9, and so on, always maintaining this same ratio of price per cup.
Let's address each option given:
- a) Yes, because the price is 3 times the number of pudding cups - this statement could indicate a proportional relationship if the price for every one pudding cup is consistently $3.
- b) Yes, because 3 times the price is the number of pudding cups - this does not make sense for a proportional relationship as it suggests that the quantity of cups should increase faster than the price, which is not the typical way we interpret price to quantity relationships.
- c) No, because the price of 4 pudding cups should be $8 and not $12 - this statement would be accurate if we were assuming that 1 pudding cup costs $2. However, if the ratio is supposed to be 1 cup costs $3, then $12 for 4 cups would be correct, and this option would not be true.
- d) No, because the price of 8 pudding cups should be $48 and not $24 - if the price was $3 per pudding cup, 8 cups should indeed cost $24, meaning this statement is incorrect if we assume the ratio is $3 per cup.
Based on this analysis, if the price per pudding cup is consistently $3 across the table, option (a) would be correct, indicating a proportional relationship.
Option (c) is also possibly correct in implying there is no proportional relationship if somehow it is inferred that the ratio should be different, like $2 per cup. Without the actual table, we can only evaluate these statements based on the information provided.