0 0
1 35
2 70
3 105
4 140
A tour bus company is planning a trip through Utah’s national parks. The company plans to use 4 buses. Combined, the buses can fit up to 140 people. The table provided displays the number of people-to-bus ratio. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.
(1 point)
To determine at which ratio in the data table the constant of proportionality appears, we need to identify a constant multiplier that relates the number of people to the number of buses.
Looking at the data table, we can see that as the number of buses increases by 1, the number of people increases by 35 (from 0 to 35, 35 to 70, 70 to 105, and 105 to 140). This consistent increase of 35 suggests that the constant of proportionality may be 35.
Therefore, the constant of proportionality appears at the ratio (1, 35).
To find the ratio at which the constant of proportionality appears, we need to examine the given data table. The data table shows the number of people in relation to the number of buses. Let's examine the pattern of the values in the table:
0 buses: 0 people
1 bus: 35 people
2 buses: 70 people
3 buses: 105 people
4 buses: 140 people
We can see that each time the number of buses increases by 1, the number of people increases by 35. This means that the ratio between the number of people and the number of buses is constant.
Let's calculate the ratios for each data point:
0 buses: 0 people -> ratio = 0/0 = undefined
1 bus: 35 people -> ratio = 35/1 = 35
2 buses: 70 people -> ratio = 70/2 = 35
3 buses: 105 people -> ratio = 105/3 = 35
4 buses: 140 people -> ratio = 140/4 = 35
From the calculations, we can see that the ratio 35 appears consistently across all the data points. Therefore, the constant of proportionality in the data table is 35.
So the answer is (35, 35) as an ordered pair.