Lesson 4
Comparing Relationships with Tables
Problem 1
Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?
- How loud a sound is depending on how far away you are.
distance to
listener (ft)sound
level (dB)5 85 10 79 20 73 40 67 - The cost of fountain drinks at Hot Dog Hut.
volume
(fluid ounces)cost
($)16 $1.49 20 $1.59 30 $1.89
Solution
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Problem 2
A taxi service charges $1.00 for the first \(\frac{1}{10}\) mile then $0.10 for each additional \(\frac{1}{10}\) mile after that.
Fill in the table with the missing information then determine if this relationship between distance traveled and price of the trip is a proportional relationship.
distance traveled (mi) | price (dollars) |
---|---|
\(\frac{9}{10}\) | |
2 | |
\(3\frac{1}{10}\) | |
10 |
Solution
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Problem 3
A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional for either one? If so, write an equation that represents the relationship.
Turtle’s run:
distance (meters) | time (minutes) |
---|---|
108 | 2 |
405 | 7.5 |
540 | 10 |
1,768.5 | 32.75 |
Rabbit’s run:
distance (meters) | time (minutes) |
---|---|
800 | 1 |
900 | 5 |
1,107.5 | 20 |
1,524 | 32.5 |
Solution
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Problem 4
For each table, answer: What is the constant of proportionality?
a | b |
---|---|
2 | 14 |
5 | 35 |
9 | 63 |
\(\frac13\) | \(\frac73\) |
a | b |
---|---|
3 | 360 |
5 | 600 |
8 | 960 |
12 | 1440 |
a | b |
---|---|
75 | 3 |
200 | 8 |
1525 | 61 |
10 | 0.4 |
a | b |
---|---|
4 | 10 |
6 | 15 |
22 | 55 |
3 | \(7\frac12\) |
Solution
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(From Unit 5, Lesson 1.)Problem 5
Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.
cups of flour | cups of water |
---|---|
1 | \(\frac12\) |
4 | |
3 | |
\(\frac12\) |
Solution
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(From Unit 2, Lesson 9.)