Use the table to answer the question.
Hours: | Money:
1 | 9
2 | 18
3 | 27
4 | 36
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship indicate why.
A. NO, the ratio of 3 hours to $27 is not proportional.
B. Yes, the ratios are in a proportional relationship.
C. No, the ratio of 1 hour to $9 is not proportional.
D. No, the ratios are not equivalent.
B. Yes, the ratios are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between hours and money are consistent.
Let's calculate the ratios between hours and money:
1 hour to $9: 1/9 = 1/9 = 0.111...
2 hours to $18: 2/18 = 1/9 = 0.111...
3 hours to $27: 3/27 = 1/9 = 0.111...
4 hours to $36: 4/36 = 1/9 = 0.111...
As we can see, all the ratios are equal to 1/9 (approximately 0.111...). Therefore, the quantities in the data table are in a proportional relationship.
The answer is B. Yes, the ratios are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio of hours to money is consistent throughout the table.
Let's calculate the ratios for each line in the table:
- Ratio for the first line: 1 hour / $9 = 1/9
- Ratio for the second line: 2 hours / $18 = 2/18 = 1/9 (which is the same as the first ratio)
- Ratio for the third line: 3 hours / $27 = 3/27 = 1/9 (which is the same as the previous ratios)
- Ratio for the fourth line: 4 hours / $36 = 4/36 = 1/9 (which is consistent with the previous ratios)
Since the ratios for each line of the table are all the same (1/9), we can conclude that the quantities in the data table are indeed in a proportional relationship.
Therefore, the correct answer is B. Yes, the ratios are in a proportional relationship.