Use the table to answer the 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.
The constant of proportionality appears when the ratio of the number of people to the number of buses is constant. In the table, we can see that as the number of buses increases by 1, the number of people also increases by 35. Thus, the constant of proportionality is (35, 1).
se the table to answer the question.
Hours Miles walked
14 1
12 2
34 3
1 4
It takes Julian 12 hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?
(1 point)
Responses
(1, 4)
left parenthesis 1 comma 4 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 14)
The constant of proportionality appears when the ratio of the miles walked to the hours taken is constant. In the table, we can see that as the miles walked increases by 1, the hours taken also increases by 12. Thus, the constant of proportionality is (1, 12).
To determine the constant of proportionality, we need to identify the ratio in the data table that remains constant. From the table, we can see that as the number of buses increases, the number of people also increases.
Let's find the ratio of people to buses for each row:
- For 0 buses, the ratio is 0 people per bus.
- For 1 bus, the ratio is 35 people per bus.
- For 2 buses, the ratio is 70 people per bus.
- For 3 buses, the ratio is 105 people per bus.
- For 4 buses, the ratio is 140 people per bus.
The ratio that remains constant is the one where the number of people per bus does not change. Looking at the table, this is the ratio of 35 people per bus.
Therefore, the constant of proportionality appears at the ratio of (1, 35) (number of buses, number of people per bus).
To identify the constant of proportionality in the data table, we need to find the ratio where the number of people per bus remains the same.
Looking at the table, we observe that as the number of buses increases, the number of people also increases. For example, with one bus, there are 35 people; with two buses, there are 70 people. Therefore, the constant of proportionality should be the ratio between the number of people and the number of buses that remains the same.
To find this ratio, we can divide the number of people by the number of buses for each row in the table:
For the first row (0 buses), the ratio is 0 people / 0 buses, which is undefined.
For the second row (1 bus), the ratio is 35 people / 1 bus, which gives us 35.
For the third row (2 buses), the ratio is 70 people / 2 buses, which also gives us 35.
For the fourth row (3 buses), the ratio is 105 people / 3 buses, which gives us 35.
For the fifth row (4 buses), the ratio is 140 people / 4 buses, which gives us 35.
Since the ratio remains the same (35) for all bus quantities, the constant of proportionality in the data table is (35, 35).
Therefore, the answer is (35, 35).
Use the table to answer the question.
Cups of Flour Loaves of Bread
1 1/2
2 1
3 1 1/2
4 2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of bread. The data table shows how much flour the bakery needs depending on the number of loaves it intends to make. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.