Use the table to answer the question.

Question

Buses Number of People
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.

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Answer 1

To find the constant of proportionality, we can look at the relationship between the number of buses and the number of people. The constant of proportionality (k) is found by expressing the ratio of people to buses.

From the table:

• When there are 1 bus, there are 35 people.
• When there are 2 buses, there are 70 people.
• When there are 3 buses, there are 105 people.
• When there are 4 buses, there are 140 people.

We can calculate the ratio for each entry:

1. For 1 bus: \[ \text{Ratio} = \frac{35}{1} = 35 \]

2. For 2 buses: \[ \text{Ratio} = \frac{70}{2} = 35 \]

3. For 3 buses: \[ \text{Ratio} = \frac{105}{3} = 35 \]

4. For 4 buses: \[ \text{Ratio} = \frac{140}{4} = 35 \]

All of these calculations reveal that the constant of proportionality is 35, meaning for every bus, it can carry 35 people.

The ordered pair representing the relationship for this point is (4, 140), because that corresponds to the maximum capacity given in the context of 4 buses.

Thus, the answer is:

(4, 140)