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.

(1 point)

Answer 1

To determine the constant of proportionality from the given table, we can analyze the relationship between the number of buses and the number of people.

From the table:

• 1 bus accommodates 35 people.
• 2 buses accommodate 70 people.
• 3 buses accommodate 105 people.
• 4 buses accommodate 140 people.

The number of people is directly proportional to the number of buses. To find the constant of proportionality (k), we can use the formula:

\[ k = \frac{\text{Number of People}}{\text{Number of Buses}} \]

Let's calculate it for one of the entries, for example when there are 4 buses:

\[ k = \frac{140}{4} = 35 \]

This ratio (35 people per bus) appears consistently in the table and demonstrates that for each bus, there are 35 people.

Therefore, the constant of proportionality appears at the ordered pair (4, 140).

So, the final answer is:

(4, 140)

Answer 2

wrong

Answer 3

I apologize for any confusion in my previous response. Let's clarify the question and work through it step-by-step to find the constant of proportionality.

The table shows the number of buses and the corresponding number of people:

• 0 buses = 0 people
• 1 bus = 35 people
• 2 buses = 70 people
• 3 buses = 105 people
• 4 buses = 140 people

The proportion can be calculated as follows:

To find the constant of proportionality \( k \), we can use the formula:

\[ k = \frac{\text{Number of People}}{\text{Number of Buses}} \]

For the first non-zero entry (1 bus):

\[ k = \frac{35}{1} = 35 \]

If we check other entries:

• For 2 buses:

  • \( k = \frac{70}{2} = 35 \)

• For 3 buses:

  • \( k = \frac{105}{3} = 35 \)

• For 4 buses:

  • \( k = \frac{140}{4} = 35 \)

This confirms that the ratio remains constant at \( 35 \) people per bus.

Answer for the asked ratio:

The constant of proportionality can be found at each point, but could be specifically cited at the point where the number of people is proportional to the number of buses that fits the question context. Generally, the simplest non-zero ratio that demonstrates this is (1, 35), meaning for 1 bus there are 35 people.

So the ordered pair reflecting the constant of proportionality based on the bus to people ratio is:

(1, 35).

I hope this clarifies the correct answer! Thank you for your patience.