Use the table to answer the guestion.
Hours Money ($)
Item 3
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
27
36
(1 point)
No. the ratio of 1 hour to $9 is not proportional
No. the ratio of 3 hours to $27 is not proportional
ltem5
Yes. the ratios are in a proportional relationship
• No, the ratios are not equivalent.
Yes, the ratios are in a proportional relationship because when the hours are multiplied by 3, the corresponding money amounts are also multiplied by 3.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios are equivalent.
For Item 3:
- The ratio of 1 hour to $9 is not proportional because if we multiply 1 by 9, we don't get 27.
- The ratio of 3 hours to $27 is not proportional because if we divide 27 by 3, we don't get 9.
For Item 5:
- The ratios are in a proportional relationship because if we multiply the number of hours by the ratio, we get the corresponding amount of money:
- For 1 hour, the corresponding amount of money is $9 (1 x 9 = 9).
- For 3 hours, the corresponding amount of money is $27 (3 x 9 = 27).
Therefore, the quantities in Item 5 are in a proportional relationship, while Item 3 is not.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the hours and the money value remain constant.
Let's start with Item 3. The table states that 1 hour corresponds to $9 and 3 hours correspond to $27. To check if this is a proportional relationship, we calculate the ratio between the hours and money:
For 1 hour: 1 hour / $9 = 1/9
For 3 hours: 3 hours / $27 = 1/9
Since the ratios are the same (1/9) for both 1 hour and 3 hours, we can conclude that the quantities in Item 3 are in a proportional relationship.
Now let's move on to Item 5. The table doesn't provide specific values for this item, but it states that the ratios are in a proportional relationship. However, it also mentions that the ratios are not equivalent. This means that while the quantities might be proportional, the specific ratio between hours and money might change, indicating a non-equivalent relationship.
In conclusion, the quantities in Item 3 are in a proportional relationship because the ratio remains constant, while the quantities in Item 5 are proportional but not equivalent because the ratios might vary.