Buses 0 1 2 3 4 Number of People 0 35 70 105 140
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.
The constant of proportionality appears at the ratio (1, 35).
To determine the constant of proportionality in the given data table, we need to identify the ratio that remains the same throughout. The constant of proportionality is the value by which one quantity increases or decreases in relation to another.
Let's examine the ratios in the data table:
For the first bus, the ratio of people to the bus is 0:0, which means there are no people on the bus.
For the second bus, the ratio of people to the bus is 35:1.
For the third bus, the ratio of people to the bus is 70:2, and so on.
To find the ratio that remains constant, we need to find a common factor between the number of people and the bus number. In this case, the common factor is the number 35. We can see that as the bus number increases by 1, the number of people also increases by 35.
Therefore, the constant of proportionality in the data table is (35, 1), indicating that for every increase of 1 in the bus number, there is a corresponding increase of 35 in the number of people.
To find the constant of proportionality in the given data table, we need to look for a consistent ratio between the number of people and the number of buses.
We can calculate the ratio for each row by dividing the number of people by the number of buses:
For bus 0: Ratio = 0 / 0 = undefined
For bus 1: Ratio = 35 / 1 = 35
For bus 2: Ratio = 70 / 2 = 35
For bus 3: Ratio = 105 / 3 = 35
For bus 4: Ratio = 140 / 4 = 35
The constant of proportionality is 35, as it appears in each row. So the answer is (35, 35).