Use the table to answer the question.
Time (min): 1 | 2 | 3 | 7 | 10 |
Water Used (gal): 5 | 10 | 15 | 35 | 50 |
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.
A. No, the ratios are not equivalent.
B. No, the table does not count consecutively.
C. No, the ratio 7 : 35 is not proportional to the other ratios.
D. Yes, the data table has a proportional relationship.
A. No, the ratios are not equivalent.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of Water Used (gal) to Time (min) are equivalent for each time interval.
Let's calculate the ratios for each time interval:
For 1 minute: ratio = 5 gal / 1 min = 5 gal/min
For 2 minutes: ratio = 10 gal / 2 min = 5 gal/min
For 3 minutes: ratio = 15 gal / 3 min = 5 gal/min
For 7 minutes: ratio = 35 gal / 7 min = 5 gal/min
For 10 minutes: ratio = 50 gal / 10 min = 5 gal/min
As we can see, for each time interval, the ratio of Water Used to Time is always 5 gal/min. Therefore, the ratios are equivalent for each time interval, which means the quantities in the data table are in a proportional relationship.
The correct answer is:
D. Yes, the data table has 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 the values are equivalent.
Let's calculate the ratios between the values:
1:5 = 1/5
2:10 = 2/10 = 1/5
3:15 = 3/15 = 1/5
7:35 = 7/35 = 1/5
10:50 = 10/50 = 1/5
As we can see, all the ratios between the values are equivalent. They all simplify to 1/5.
Therefore, the answer is D. Yes, the data table has a proportional relationship.