Hours: 1 2 3 4
Money ($): 9 18 27 36
Determine if the quantities in the data are in a proportional relationship. If they are not in proportional relationship, indicate why.
Yes, the ratios are in proportional relationship
No, the ratio of 1 hour to $9 is not proportional
No, the ratio of 3 hours to $27 is not proportional
No, the ratios are not equivalent
The ratios in the data are not in a proportional relationship. Each hour does not correspond to the same amount of money. Therefore, the ratios are not equivalent and the quantities are not proportional.
To determine if the quantities in the data are in a proportional relationship, we need to check if the ratios between the hours and the money are consistent.
Let's calculate the ratios for each pair of values:
For the first pair (1 hour and $9): 1/9 = 0.1111...
For the second pair (2 hours and $18): 2/18 = 0.1111...
For the third pair (3 hours and $27): 3/27 = 0.1111...
For the fourth pair (4 hours and $36): 4/36 = 0.1111...
As we can see, the ratios for each pair of values are equal to 0.1111... which means that they are consistent. Therefore, the quantities in the data are in a proportional relationship.
To determine if the quantities in the data are in a proportional relationship, we need to check if the ratios between the hours and the money amounts are constant.
First, let's calculate the ratios between the hours and money amounts:
- The ratio of 1 hour to $9 is 1:9.
- The ratio of 2 hours to $18 is 2:18, which simplifies to 1:9 as well.
- The ratio of 3 hours to $27 is 3:27, which simplifies to 1:9 as well.
- The ratio of 4 hours to $36 is 4:36, which simplifies to 1:9 as well.
As we can see, all the ratios simplify to 1:9, which means they are constant. Therefore, the quantities in the data are in a proportional relationship.
Note: If any of the ratios did not simplify to the same constant ratio, then the quantities would not be in a proportional relationship. In this case, since the ratios are constant and equal to each other, we conclude that the quantities are proportional.