Buses 0 1 2 3 4 Number of people 0 35 70 105 140 A tour bus company is planning a trip through utah 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
In the given data, the number of people increases by 35 each time the bus number increases by 1. This constant increase suggests that the constant of proportionality is 35.
The ratio in the data table at which the constant of proportionality appears can be determined by dividing the number of people by the number of buses. Let's calculate this for each row in the table:
For the first row:
Number of people = 0
Number of buses = 0
Ratio = 0/0 = undefined
For the second row:
Number of people = 35
Number of buses = 1
Ratio = 35/1 = 35
For the third row:
Number of people = 70
Number of buses = 2
Ratio = 70/2 = 35
For the fourth row:
Number of people = 105
Number of buses = 3
Ratio = 105/3 = 35
For the fifth row:
Number of people = 140
Number of buses = 4
Ratio = 140/4 = 35
As we can see, the ratio of the number of people to the number of buses is constant at 35 for all rows except the first row where it is undefined. Therefore, the constant of proportionality appears at a ratio of 35 in the data table.
To find the ratio where the constant of proportionality appears in the data table, we need to identify a ratio where the number of people is directly proportional to the number of buses.
In this case, we can look for a ratio where the number of people increases or decreases by a constant factor each time the number of buses increases by 1.
Let's examine the ratios:
0:0 (No people and no buses)
35:1 (35 people for 1 bus)
70:2 (70 people for 2 buses)
105:3 (105 people for 3 buses)
140:4 (140 people for 4 buses)
Here, we see that the number of people increases by 35 each time the number of buses increases by 1. Therefore, the constant of proportionality is 35.
So, the ratio where the constant of proportionality appears in the data table is 35:1.