A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parenthesis provided.
Number of cases ordered,
1,3,5,10
Number of rolls of paper towels,
12,36,60,120
The constant of proportionality appears in the ratio (3, 36), since when the number of cases ordered increases by a factor of 3, the number of rolls of paper towels also increases by a factor of 3.
wrong
Apologies for the mistake. Let's find the correct answer.
To find the constant of proportionality, we need to identify the ratio in the data table where the number of rolls of paper towels is directly proportional to the number of cases ordered.
Let's calculate the ratios for each case:
- Ratio 1: (3, 36) -> 36/3 = 12
- Ratio 2: (5, 60) -> 60/5 = 12
- Ratio 3: (10, 120) -> 120/10 = 12
From this, we can see that the constant of proportionality is 12 because the ratio remains the same (12) for all values of cases ordered. Thus, the answer is (1, 12).
not a correct answer
I apologize for the confusion.
Let's calculate the ratios for each case:
- Ratio 1: (1, 12) -> 12/1 = 12
- Ratio 2: (3, 36) -> 36/3 = 12
- Ratio 3: (5, 60) -> 60/5 = 12
- Ratio 4: (10, 120) -> 120/10 = 12
As we can see, the constant of proportionality appears in all ratios. The constant of proportionality is 12. Therefore, the answer is (12, 12).
12,12, 1,12, and 3,36 are wrong think of new answers
Apologies for the confusion earlier.
To find the constant of proportionality, we need to identify the ratio in the data table where the number of rolls of paper towels is directly proportional to the number of cases ordered.
Let's calculate the ratios for each case:
- Ratio 1: (1, 12) -> 12/1 = 12
- Ratio 2: (3, 36) -> 36/3 = 12
- Ratio 3: (5, 60) -> 60/5 = 12
- Ratio 4: (10, 120) -> 120/10 = 12
From the calculations, we can see that the constant of proportionality is indeed 12, as each ratio is equal to 12. Therefore, the answer is (12, 12).
wrong
I apologize for the repeated mistakes. Let's approach this step by step to find the constant of proportionality:
The constant of proportionality \( k \) can be found using the ratio of the number of rolls of paper towels to the number of cases ordered. If the ratio remains consistent across all pairs, that ratio is our constant of proportionality.
To find out if the ratio is constant, we need to divide the number of rolls of paper towels by the number of cases ordered for each entry and check if we get the same result every time:
For the first entry:
\[ \frac{12 \text{ rolls}}{1 \text{ case}} = 12 \]
For the second entry:
\[ \frac{36 \text{ rolls}}{3 \text{ cases}} = 12 \]
For the third entry:
\[ \frac{60 \text{ rolls}}{5 \text{ cases}} = 12 \]
For the fourth entry:
\[ \frac{120 \text{ rolls}}{10 \text{ cases}} = 12 \]
Since the ratio is consistently 12 rolls per case, the constant of proportionality \( k \) is 12. All the ratios show that for every 1 case ordered, there are 12 rolls of paper towels. Therefore, (1, 12) is the ordered pair that represents the constant of proportionality in the context of the question.