A restaurant is placing an order for paper towels. The data table shows the amount of paper towels rolls compared to the number of cases. At which ratio in the data table does the constant proportionality appear?
1:12
3:36
5:60
10:120
The constant proportionality appears in the ratio 1:12. This means that for every 1 case of paper towels, there are 12 rolls.
To find the ratio in the data table where the constant proportionality appears, we need to identify where the ratio remains the same.
Let's calculate the ratio for each option:
1:12 = 1/12 ≈ 0.083
3:36 = 3/36 = 0.083
5:60 = 5/60 = 0.083
10:120 = 10/120 = 0.083
As we can see, the ratio remains the same for all options, which is approximately 0.083. Therefore, the constant proportionality appears in all the given ratios.
To determine which ratio in the data table exhibits a constant proportionality, we need to check if the ratio between the number of rolls and the number of cases remains the same throughout. We can do this by finding the unit rate for each ratio.
Let's calculate the unit rates for each ratio by dividing the number of cases by the number of rolls:
1:12 --> 1/12 ≈ 0.0833
3:36 --> 3/36 ≈ 0.0833
5:60 --> 5/60 ≈ 0.0833
10:120 --> 10/120 ≈ 0.0833
As you can see, all the ratios have the same unit rate of approximately 0.0833. This means that the proportion between the number of rolls and cases is constant for all the provided ratios.
Therefore, the constant proportionality appears in all of the ratios: 1:12, 3:36, 5:60, and 10:120.