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.

Answer 1

To find the constant of proportionality for the data in the table, we can examine the number of people each bus can hold. The number of people increases linearly with each additional bus.

From the table:

• 1 bus → 35 people
• 2 buses → 70 people
• 3 buses → 105 people
• 4 buses → 140 people

To find the constant of proportionality (k), we can divide the number of people by the number of buses for any of the entries:

Using the first entry from the data: \[ k = \frac{35}{1} = 35 \]

Using the second entry: \[ k = \frac{70}{2} = 35 \]

Using the third entry: \[ k = \frac{105}{3} = 35 \]

Using the fourth entry: \[ k = \frac{140}{4} = 35 \]

In each case, the constant of proportionality is the same: \( k = 35 \).

The ordered pair representing this relationship, where the first number corresponds to the number of buses and the second corresponds to the number of people, is: \((1, 35)\).

Thus, the answer is: \((1, 35)\)